diff --git a/.gitignore b/.gitignore index c63343e7..07677455 100644 --- a/.gitignore +++ b/.gitignore @@ -9,3 +9,8 @@ dist/ build/ .agent-memory-cache/ .DS_Store + +# Rights-restricted local source artifacts. Keep checksums and derived work, +# but never distribute the publisher PDF or its verbatim extraction in Git. +/proposals/P229-preparata-qcd-vacuum-audit/sources/preparata1986-nuovo-cim-a96-366.pdf +/proposals/P229-preparata-qcd-vacuum-audit/sources/preparata1986-extracted.txt diff --git a/memory/codex/efforts/public-contribution-readiness.md b/memory/codex/efforts/public-contribution-readiness.md index e2f5a97e..6d82bf3c 100644 --- a/memory/codex/efforts/public-contribution-readiness.md +++ b/memory/codex/efforts/public-contribution-readiness.md @@ -2,7 +2,7 @@ description: Prepare substrate-framework for safe public contributions with explicit rights, CI, security policy, and protected-main governance author: codex-public-readiness created: '2026-08-18T09:40:10+02:00' -updated: '2026-08-18T11:10:00+02:00' +updated: '2026-08-18T12:20:00+02:00' tags: - substrate-framework - effort @@ -20,20 +20,20 @@ This effort delivers a safely public, contribution-ready `vantasnerdan/substrate Work starts from `main` commit `1b00c3a` and accepted release `v0.160.0`. The normative local sources are `AGENTS.md`, `AGENTS_START_HERE.md`, the existing issue and pull-request templates, GitHub repository settings, and exact external rights metadata. Zenodo record `10.5281/zenodo.21879560` states that `incoming/einbein_1plus1D_tutorial.pdf` is open access under `GPL-3.0-or-later`. Crossref metadata for `10.1007/BF02833896` supplies Springer text-and-data-mining terms, not verified redistribution permission for the publisher PDF or its full extracted text. ## Constraints and Invariants -Publication must not expose secrets or material lacking redistribution permission. The user selected Apache-2.0 and designated `vantasnerdan`, `axis-marbell`, and `mlops-kelvin` as the only merge-authorized maintainers whose CODEOWNER approval may satisfy the protected-main review gate. The user has not authorized a history rewrite/force-push; that materially different owner decision remains gated. Existing accepted scientific authority, immutable campaigns, generated documentation, and PR #77 are outside the implementation write boundary. Every file-change PR requires issue #78, uses `Advances #78` while publication remains incomplete, and is merged only by a distinct reviewer/owner. The original worktree's untracked `.claude/` and `CLAUDE.md` are preserved. +Publication must not expose secrets or material lacking redistribution permission. The user selected Apache-2.0 and designated `vantasnerdan`, `axis-marbell`, and `mlops-kelvin` as the only merge-authorized maintainers whose CODEOWNER approval may satisfy the protected-main review gate. On 2026-08-18 the user explicitly authorized an all-ref rewrite/force-push limited to the Preparata publisher PDF and its verbatim extraction; every derived contribution and all provenance must remain. Existing accepted scientific authority, immutable campaigns, generated documentation, and PR #77 remain semantically unchanged, while commit identifiers receive a durable translation map. Every file-change PR requires issue #78, uses `Advances #78` while publication remains incomplete, and is merged only by a distinct reviewer/owner. The original worktree's untracked `.claude/` and `CLAUDE.md` are preserved. ## Decomposition Work proceeds through these dependency-ordered steps and continues after failed attempts. 1. [x] Audit GitHub settings, community profile, all refs, contributor metadata, bundled documents, secrets, and rights provenance. 2. [x] Create canonical issue #78 and claim an isolated branch/write boundary. -3. [ ] Add contribution, conduct, security, CI, dependency, and scanner configuration without changing scientific authority. -4. [ ] Validate the documentation/workflow boundary and open a non-self-merged PR. -5. [ ] Land the owner-selected Apache-2.0 license and obtain the remaining history-sanitization decision; execute the approved rights-safe strategy. +3. [x] Add contribution, conduct, security, CI, dependency, and scanner configuration without changing scientific authority. +4. [x] Validate the documentation/workflow boundary and land independently merged PR #79. +5. [ ] Execute authorized strategy A, retain private recovery artifacts, and publish the commit-translation handoff. 6. [ ] Make the repository public, apply protected-main/security settings, and verify through a fresh anonymous clone. ## Publication Strategy Alternatives -Selection is blocked pending explicit owner authority because the alternatives have materially different provenance and collaboration effects. +The owner selected candidate A with a removal boundary limited to the two nonredistributable source artifacts. The alternatives remain recorded because they explain the decision and its costs. | Candidate | Construction | Benefit | Cost or blocker | Selection evidence | | --- | --- | --- | --- | --- | @@ -50,6 +50,7 @@ Attempts are append-only and individually reproducible. | --- | --- | --- | --- | --- | --- | | 0001 | Redacted all-history and filesystem secret scan | `ghcr.io/gitleaks/gitleaks:v8.30.1 detect` on 706 commits/all refs and the detached main worktree | Qualified pass | One `generic-api-key` hit is a plain 28-character identifier list under YAML key `public_api`, with no URL/assignment/credential structure; all other rules clean | Add a narrow scanner allowlist with documented false-positive provenance and run CI scan | | 0002 | Rights and community-surface audit | GitHub API community/settings queries, file inventory, Zenodo/Crossref metadata | Blocked publication | No project license; paywalled Preparata PDF/full extraction are reachable; CI/security/community files and branch protection are absent | Implement reversible readiness files, then obtain owner legal/history choices before visibility mutation | +| 0003 | Candidate A disposable-mirror rewrite | `git-filter-repo` 2.47.0 over 752 commits and 90 refs, removing exactly two paths | Verified rewrite candidate | 113 commits change identity; preservation oracle confirms authors, committers, timestamps, mapped parents, hash-only message rewrites, and every other blob match | Land tip deletion/ignore guard, replay the final remote boundary, then force-push verified branch refs | ## Validation - Rights/secret oracle: redacted Gitleaks all-ref history scan plus filesystem/archive scan; exact Zenodo/Crossref metadata and tracked-source inventory. @@ -65,21 +66,21 @@ Every unresolved item inside the requested public outcome remains debt until dis | Debt | Introduced by | Why it is real | Discharge artifact | Status | | --- | --- | --- | --- | --- | -| Owner-selected project and documentation license absent | Repository baseline | Public availability alone grants no reusable software rights and cannot define contribution licensing | Apache-2.0 `LICENSE`, package metadata, contribution terms, and third-party notices | in progress | -| Preparata publisher PDF and full extracted text reachable in history without verified redistribution permission | Commit `81df095` and descendants | Public Git history would redistribute the complete paywalled work | Written permission or owner-approved verified purge/mirror strategy | open | -| History rewrite/mirror authority absent | Safety boundary | Purging all refs is destructive, changes commit IDs, and affects open PRs/collaborator clones | Explicit owner decision and coordination/migration plan | open | -| Contribution/security/CI surfaces missing | Repository baseline | External contributors lack policy and automated feedback | Issue-backed PR with validated files and workflow | in progress | +| Owner-selected project and documentation license absent | Repository baseline | Public availability alone grants no reusable software rights and cannot define contribution licensing | Apache-2.0 `LICENSE`, package metadata, contribution terms, and third-party notices | discharged by PR #79 | +| Preparata publisher PDF and full extracted text reachable in history without verified redistribution permission | Commit `81df095` and descendants | Public Git history would redistribute the complete paywalled work | Verified all-ref rewrite plus GitHub cached-ref cleanup | in progress | +| History rewrite/mirror authority absent | Safety boundary | Purging all refs is destructive, changes commit IDs, and affects open PRs/collaborator clones | Explicit owner authorization on 2026-08-18 and issue #78 handoff | discharged | +| Contribution/security/CI surfaces missing | Repository baseline | External contributors lack policy and automated feedback | Independently merged and hosted-CI-verified PR #79 | discharged | | `main` unprotected, nondesignated collaborators retain write, and security features are disabled | Private/free GitHub state | Direct pushes, undesignated merge authority, and unscanned dependencies/secrets remain possible | Post-public protection, collaborator-permission reduction, and security API verification | open | | Contributor email metadata will become public | Existing Git history | Commit metadata contains personal/domain email addresses | Owner confirmation or explicitly approved author-rewrite strategy | open | ## Results -The owner selected Apache-2.0 and limited qualifying CODEOWNER review and merge authority to `vantasnerdan`, `axis-marbell`, and `mlops-kelvin`. Automatic deletion of exact same-repository heads after merge is enabled; a branch/PR reconciliation found no retained merged heads, while open and closed-unmerged/failed heads remain preserved. Discussions are enabled. Actions are restricted to GitHub-owned actions, immutable SHA pins are enforced, the default workflow token is read-only, and workflows cannot approve pull-request reviews. The `dependencies` label required by Dependabot now exists. Preflight established that the repository is private, `main` is unprotected, security scanning/update features are disabled, and no CI workflow exists on `main`. The all-history scan found no credential leak after adjudicating one identifier-list false positive. Rights review identified the exact publication-blocking source artifacts and confirmed the independent Zenodo tutorial's open GPL provenance. +The owner selected Apache-2.0 and limited qualifying CODEOWNER review and merge authority to `vantasnerdan`, `axis-marbell`, and `mlops-kelvin`. PR #79 landed independently at merge commit `e21bb8b` after local and hosted full validation; its head was automatically deleted. Discussions are enabled. Actions are restricted to GitHub-owned actions, immutable SHA pins are enforced, the default workflow token is read-only, and workflows cannot approve pull-request reviews. The `dependencies` label required by Dependabot exists. A verified private bundle with all 91 branch/PR refs and separate owner-private source copies make the pre-public state recoverable. The first disposable rewrite removes only the two authorized source blobs and preserves every other blob and contributor metadata across all 113 identity-changing commits. The repository remains private and unprotected until final-ref replay and GitHub cached-ref cleanup complete. ## Canonicalization This effort changes no scientific claim, release manifest, campaign, migration disposition, or generated scientific documentation. Durable coordination lives in issue #78, this effort record, the eventual contribution-readiness PR, and GitHub settings evidence. Any history transaction must separately migrate commit-pinned provenance before execution. ## Done Gate -The effort remains active. Contribution files, the owner history decision, a distinct merge, public visibility, branch protection/security/collaborator settings, and anonymous-clone verification are all still outstanding. +The effort remains active. The final remote-boundary rewrite, GitHub cached-ref cleanup, public visibility, branch protection/security/collaborator settings, and anonymous-clone verification remain outstanding. ## Cross-References - Canonical issue: https://github.com/vantasnerdan/substrate-framework/issues/78 diff --git a/proposals/P229-preparata-qcd-vacuum-audit/sources/README.md b/proposals/P229-preparata-qcd-vacuum-audit/sources/README.md new file mode 100644 index 00000000..3bd28a1b --- /dev/null +++ b/proposals/P229-preparata-qcd-vacuum-audit/sources/README.md @@ -0,0 +1,22 @@ +# Preparata 1986 source access + +The P229 proposal, derivations, tests, attempts, results, checksums, and +provenance remain in this repository. The publisher PDF for Preparata's 1986 +paper and its verbatim text extraction are deliberately not distributed. + +To reproduce an equation-level source audit, obtain a lawful copy through + and place local working files at: + +- `preparata1986-nuovo-cim-a96-366.pdf` +- `preparata1986-extracted.txt` + +Both names are ignored by the repository. Do not force-add or redistribute +them. Expected SHA-256 checksums for the owner-held source copies are: + +```text +d712d4a085582ac390701e0a1f43bf21796f0971eda9f355c48da8b0d98b5b8a preparata1986-nuovo-cim-a96-366.pdf +2cb0a6ca8b929d3e1513a27351173cbe05b354c1bcbc878ccaee77092c2dc961 preparata1986-extracted.txt +``` + +`MD5SUMS` is retained as immutable acquisition provenance. A checksum +identifies the audited bytes but does not grant redistribution rights. diff --git a/proposals/P229-preparata-qcd-vacuum-audit/sources/preparata1986-extracted.txt b/proposals/P229-preparata-qcd-vacuum-audit/sources/preparata1986-extracted.txt deleted file mode 100644 index 3e0222b7..00000000 --- a/proposals/P229-preparata-qcd-vacuum-audit/sources/preparata1986-extracted.txt +++ /dev/null @@ -1,981 +0,0 @@ -IL NUOVO CIMENT0 VOL. 96 A, N. 4 21 Dicembre 1986 -Essential Quantum Instability of the Perturbative -Yang-Mills Vacuum. -G. PREPARATA (*) -Istituto .Nazionale di Fisica Nucleate - ,Saboratori Nazionali di Fraseati, ]talia -(ricevuto il 24 Settembre 1986) -Summary.- We prove that there exist gauge field configurations -whose energy density is lower than that of the perturbative Yang-Mills -vacuum by a quantity AE~ bA 4 (A is the ultraviolet cut-off) where b -remains finite when g-+ 0. This striking physical situation, which pre- -vents the use of perturbation theory even at extremely short distances, -is what has been called essential instability. -PACS. 11.10. - Field theory. -l. - Introduction. -The question of the stability of the classical ground state (zero field) of the -non-Abelian Yang-Mills theory under quantum fluctuations has attracted the -theorists' attention since a long time. To our knowledge SAVVIDu (2) was -the first to point out in 1977, within the one-loop approximation to the effec- -tive potential of a pure SU2 Yang-Mills theory, that due to quantum fluctuations -the classical ground state (i.e. the perturbative ground state) does not cor- -respond to a local minimum of the energy density, and a local minimum was -found for constant (chromo-)m~gnetic field H* (Savvidy's state) -24~2 ] -(1.1) gH* _~ A2 exp 11~-A)J ' -(*) On leave of absence from: Dipartimento di Fisica dell'Universits di Bari, Italy. -(1) G.K. SAVVIDY: Phys. Left. B, 71, 133 (1977). -366 - - -=== PAGE BREAK === - -ESSENTIAL QUANTUM INSTABILITY ETC. 367 -A 2 being the ultraviolet cut-off. The interest of (1.1) lies in its perfect consistency -with the renormalization group requirement; indeed, solving (1.1) for g2(A), -one gets the well-known asymptotic freedom (AF) expression of g~(A). -Subsequently, Savvidy's calculation was found to contain a basic flaw (3), -in that the state he found was itself ~mstable due to a peculiar feature of the -dynamics of gauge fields in an external constant magnetic field. As shown -by LANDAU in the early 30% the energy spectrum of a charged relativistic par- -ticle in a eostant magnetic field H in the z-direction is given by -(1.2) E~(p,) = [p~. + gH(2n -~ 1) -- 2gllS~]i . -For 181>1, (1.2) implies the existence of a portion of the spectrum (n = 0, -Sz = 1, IP~I < (gH)~) with imaginary energy, thus signalling a basic instability. -A considerable amount of work has been devoted to try and understand -the effect of such an instability on the perturbative vacuum, and its possible -role in the fnndamental property of color confinement. However, only re- -cently (s) it has been possible to go effectively beyond a somewhat heuristic -stage, by use of a variational approach based on Gaussian wave funetionals, -endowed with perturbative (in g) gauge invariance. As we shall describe in -sect. 2, the first results that were obtained have been rather surprising, showing -the existence of a Savvidy's state where the energy density has a local minimum -for a value of the magnetic field -(1.3) gH*--. A s exp [-- 12~z~/llg2(A)] , -which does not agree with the AF prediction (1.1). As a consequence the long- -distance properties of the theory, that should be responsible for eolour con- -fmement, cannot be in agreement with perturbation theory (PT). For, if AF -were right, by inserting the AF prediction of g2(A) in (1.3) one would obtain -a divergent (~-- A) magnetic field and an equally divergent (~ A 2) energy density -gap with respect to the perturbative ground state. Divergences that on the -real ground state can only be more severe, due to the variational nature of our -calculation. -The calculation of ref. (3) did not, however, exhaust the possibilities of the -variational techniques developed and a fully consistent calculation which takes -into account all terms to O(g ~) was still lacking. In particular, the very im- -portant point of whether the interaction between the unstable modes and the -stable modes (for which En in (1.2) is real) could change our conclusions was -only argued in the negative, but not conclusively established. -(2) N.K. :NIELSEN and P. 0LESE~: Nucl. Phys. B, 134, 376 (1978). -(~) M. CONSOLI and G. PREPARATA: Phys. Left. B, 154, 411 (1985). - - -=== PAGE BREAK === - -368 o. PREPARATA -This paper intends to fill the gaps loft by the previous work in two dif- -ferent directions: to give a full two-loop analysis of the variational calculation, -and to establish the (~ nourenormalization ~> of the nonperturbative effects due -to the unstable modes. In the course of our two-loop analysis a new term in -the energy density was found whose effect is even more striking than (1.3). -I shall indeed prove that the Savvidy's state with minimum energy must be -associated with a magnetic field gH* which is proportional to A *, the constant -of proportionality being finite when g2_> 0. -Thus, there exists no choice of g* such that for scales smaller than a finite -scale the perturbative ground state is a good representation of the real ground -state. I have called this disquieting phenomenon the essential quantum instability -of the perturbative ground state. I shall briefly comment about the drastic -consequences of this result on the prevailing picture of Yang-Mills theories -at the end of this paper. -Let me finally mention that this approach has been recently criticized (*). -It is hoped that this paper will give convincing evidence of the unfoundedness -of those criticisms. -2. - The original variational calculation. -In ref. (8) a variational calculation was presented of the energy density -of the trial state (I adopt here the same notations of that paper) -(2.1) ~[A ~] = G[~']F[~] , -where the gauge field in the timelike gauge A~'(x) (a= 1 2, 3, SU, index) -is written as -A~(x) =f~(x) + ~(x), -and f" is chosen to represent a chromomagnetic field along the z-direction and -in the 3-direction of isospace, i.e. modulo a gauge transformation one has -(2.3) ]~(x) = ~ t'~Hx,. -In eq. (2.1) G[~ ~] is a Gaussian wave functional -(2.4) -(4) L. MAIANI, G. MARTINELLI, G. ROSSI and M. TESTA: A constant chromomagnetic -field leads nowhere, Rome preprint (November 1985). - - -=== PAGE BREAK === - -ESSENTIAL QUANTU~I INSTABILITY ETC. 369 -where the inverse propagator G-~g~(x, y) contains an infinite number of va- -riational parameters (see eq. (2.13)). The functional F[~ ~] is a finite-degree -polynomial in the fields ~l, chosen in such a way as to implement the approx- -imate requirement of gauge invariance: -(2.5) {D~(]) + gs=~,v~(x)} ~ ~[v] = o, -where the covariant derivative D~(]) is given by -(2.6) D;~(]) = ~ ~k q- ge~Pv ]~(x) 9 -Recalling that in the present SchrSdinger formalism the electric field E~(x) = --= -- i~/(5~(x), we immediately recognize in (2.5) the Gauss law. -In order to evaluate the energy density of the state (2.1), one first writes -down the energy density as -(2.7) .YF(x) ---- 89 ~ [E~"(x) + B2~(x)], -where -(2.s) Acr -and then one computes the expectation value of the operator (2.7), on the -state (2.1). However, here we encounter a first problem for, as is well known, -after having fixed the timelike gauge we have still at our disposal a time- -independent gauge transformation. This circumstance makes it impossible -to define on the space of gauge-invariant states a scalar product that is nor- -malizable. The way out of this difficulty is well known (5); fix a three-dimen- -sional gauge (which for convenience we shall take D~(f)~(x)---- 0) and write -the scalar product as -(2.9) @I~> ----f[dn] 1-I 8(Dr/)A[r/] ~p*[r/](p[r/], x -where A[r/] is the Faddeev-Popov determinant, associated with our gauge- -fixing, which is evaluated in appendix A. It turns out, however, that the Fad- -deev-Popov determinat plays no role in our calculation. The last ingredient -we need in order to complete the calculation of ref. (3) is a technique to solve -the contraints imposed by the Gauss law (2.5). From the detailed analysis -reported in appendix ]3, we learn that we can represent the logarithm of the -(5) L.D. FADDEEV and V. N. PoPov: Phys. Left. B, 25, 29 (1967). - - -=== PAGE BREAK === - -370 ~. PR~PARATA -functional F[~] as a power series in the coupling constant g: -(2.~0) in F[V] ---- ~ g~ W~+~)[V], -where the functionals W ~+~) are monomiMs in the fluctuating field ~(x) of -degree k + 2, whose explicit form can be obtained from a set of recursive equa- -tions. In ref. (~) only the lowest-order contribution, 0(g2), to the energy density -has been considered, implying that on our wave functional the Gauss law is -satisfied to the same order. -From the results of appendix B one readily derives for the energy density -E(H) the following expression (V is the volume of the system): -(2.11) E(H) : 1/V >(gH) t) in such a way that the S-modes for which Ex>Eo -shall be treated perturbatively, while those with E~ < Eo are analysed va- -riationally. Thus we shall decompose the fluctuating field ~Y(x) as -(3.1) VT(x)=hT(x)+lT(x), -where h~(x) contains the modes with E~>/~0--the h-modes--, while l~.(x) -is built up by the S-modes with EN < Be and by the U-modes, which will be -globally called /-modes. -The functional _P[~] appearing in (2.]) will be improved as follows: -(3.2) rill = (1 + #,~,[v]) exp [gW'~'[v]], -where the functional 5(a)[V], differently from W(a)[~], contains transverse fields -only. 8r is further decomposed as -(3.3) -~(a) contains two /-modes where v 1~(3~ contains one /-mode and two h-modes, and ~2 -and one h-mode. -Let us begin with ~[~]. We write -(3.4) ~[3) __ ~/~.~1 fJ[ili~iZl~2a (X1 -XlX2X -, x~, x) aT:(x~)* aT:(x~)* bT(x)*, -where one has introduced the creation operators for the h-modes --fH (3.5) a?(x)* = 1/2 hT(x) 7f(x, y) Shf(x) ' -Y -and for the 1-modes, -(3.6) b~Y(x)f ~- 1/2 l~(x) 7(x, :y) ~l~(x) ' -Y -and the propagator is decomposed as -(3.7) GTf(x , y) : ZTf(x, y) + H~f(x, y). -Up to O(g ~) the matrix elements we must consider are those of the quadratic -(H2) and cubic (H3) parts of the Hamiltolfian, which we compute in appendix C. - - -=== PAGE BREAK === - -ESSENTIAL QUANTUM INSTABILITY ETC. 375 -Note that in our calculation only the quadratic Hamiltonian --3/~) of the h-modes -is needed, for the contribution of H It) (*) can be absorbed in a redefinition of --3 -the propagator Z, which is to be determined variationally. -One notes immediately that the amplitudes A ..... appear quadratically iti~i -in the matrix element of H~ but only linearly in H a . -By minimizing with respect to such amplitudes, we get (eq. (C.6)) -(3.8) -with -(3.9) -and -(3.10) -"/" i'~'(#,#,Wv;v3v). A~:?y(x~, x~, x) = - ~j~,~,,,, ,.,.,., -Y~Y~Y - 9 (~)~,,, (y~, x~)(~ )~,~, (yl, x~)(L-~)~?(x, y) --Kr xz, x) = 1/2[K~,~:;~'(XlX3, x) + (1 e-+ 2)] -K~,~:2C'(x~, x3, x) ~v/2.a f{D.(~)~.~,(~, x)~';;'(~, Xl)Uk~'(~ 9 X2) + -+ Dts n~ ~ , x1)(lt';:'(z, -" 'L'~'z x) + n'~lz ~J ~,t , ~. , , x3)~:(~, ~)) -The contribution E (3) to the energy density is --1 -(3.11) E? ) - x)(a),.j. (x,, y.)~-'~;~'(~3 y3)" -XlXaX -Y'Y~Y .L~#(x, y)K c~'#')~l~, y~, Y) -The structure of E~ 3) is worth noting. Indeed we can associate to it the -diagram reported in fig. la), where K is the two h- and one /-modes' unam- -putated vertex and the two-body operator ~ represents the insertion of the -quadratic ttamiltonian t7 (h) The interest of this observation lies in the not --2 " -6 6 -\ L -I // -a) b) -Fig. 1. - The diagrammatic interpretation of a) (3.11), and b) (3.13). Continuous lines -represent h-modes, while dashed lines represent /-modes. -(*) According to the discussion above, the high-frequency part H~f(x, y) is given by -its lowest-order expression H~f = ~_, 1/2E,v y~y,*~. - - -=== PAGE BREAK === - -376 c,. PREPARATA -too surprising fact that the solution of our variational problem in the presence -of a small parameter (g) exhibits a perturbative structure (*). -As for ~), the wave functional containing two /-modes and one h-mode, -one writes -(3.12) 5(3,: 1/V'~. (B!%~!~(xl. x) b~'(xl)+b~(x2)+a?(x) ~ . X2 -Proceeding exactly as before for the contribution E m) to the energy density, --2 -we obtain -(3.13) --3F'(a) ~ -- ~2/A Tr ~'T(++++)+/,,. +~/.L -1 x+~P~ / x .'Yl) (L-1)i.:~++"/5'" (X2, ~2) " F:i:u i ~1, "~2, ,a~]~ ]il~l ~ 1, -XlXSX -Y~Y2Y - 9 ~f(x, ~ ~ r l~'~)~x. ,,J~(j,~,)~ , ,Y2, Y), -where for LCc++,.,:,,),:)~/x~ 1, x2, x) one derives an expression identical to (3.9), and -(3.10) with L/f and H~f interchanged. The diagram associated with (3.13) -is depicted in fig. lb). -At this point all we need to do in order to complete our calculation is to -evaluate E (3) and ~m) a task that requires a substantial amotmt of labor, which --1 ~2 ' -can luckily be saved, as we shall demonstrate in the next section. -Two crucial features of these contributions, however, can be established -without too much effort. The first has to do with the question of the cancel- -lation of the quadratic divergences contained in (2.11). A straightforward -calculation (appendix D) shows that the quadratic divergences contained in -E(m are precisely right to compensate those appearing in (2.11), thus imple- 1 -menting a basic requirement of full fledged gauge invariaace. -The other crucial feature is the presence in E (3) of a term (see appendix D) --2 -(3.14) H2q~e -that cancels half of the positive and << stabilizing >> contribution of the U-modes -to the quartic part of the ttamiltonian. -As a result the full contribution E~ to the energy density of the U-modes, -replacing (2.16), is -(3.~ ~) E~ = -- '-7 u-- , -(*) Incidentally our construction shows that the Rayleigh-Ritz approximation in the -Schr5dinger picture can be systematically improved by means of a perturbationlike -expansion (7). -(7) J.N. CORNWALL, R. JACKIW and E. T. TO~BOULIS: -Phys. Rev. D, 1, 2428 (1974). - - -=== PAGE BREAK === - -ESSENTIAL QUANTUM INSTABILITY :ETC. 377 -whose minimum occurs at u* = 2 and equals -H 2 -(3.16) Evmin -- 2 ' -thus completely cancelling the classical energy density! Neglecting the inter- -action between S-modes and U-modes, as it shall be fully justified in the next -section, the energy density of our trial state is -(3.17) llg2H ~. [A~\ E(H) : E(O) ~ m t-g-~) -~ O(g~H2). -This is the central result of this paper and the basis of the contention that -the perturbative ground state of a u theory is essentially unstable. -Even though we have not proved that our state is the real ground state, we -have nevertheless demonstrated that there exists a perfectly well-defined and -respectable configuration of the gauge fields whose energy density is infinitely -(when A -~ cr lower than that of the perturbative ground state. Indeed the -disappearance from (3.17) of the classical term implies that the minimum oc- -curs at H* ~ A 2 and the energy difference at the minimum is given by E(0) -- --- E(H*)~A 4. Given this very extreme situation, in no circumstance can the -perturbative ground state be a good approximation to the real ground state, -for the real ground state must be lower in energy than our state, which is already -infinitely (when A-+ ~c) distant from the perturbative one. We hope that -this brief discussion provides a sufficiently clear illustration of the rather unusual -notion of essential instability. We shall, however, resume this discussion in the -final section. -4. - The essential instability survives renormalization. -Let us first summarize the consequences of the improved variational ansatz -that we have just described: -i) The contribution to the energy density of the U-modes takes the -form -(4.1) -corresponding to the diagrams in fig. 2. -ii) All quadratic divergencies to O(g 2) cancel. -iii) The coupling of the U-modes to the S-modes induces logarithmic -corrections O(g ~ In A~/gH) to both the u- and the uS-term, whose coefficient -can be computed directly with a considerable amount of labor. - - -=== PAGE BREAK === - -378 G. PR~PARATA -U U-1 -# -X~\ i / \\ -+ .,.--~. + -U , /I \ ~. // -U-I U -Fig. 2. - Diagrams contributing to E~ (eq. (4.1)). The dashed lines correspond to -U-modes. -iv) While for the logarithmic corrections to the u-term our ansatz ex- -hausts them, for the u"-term the situation is different. One gets in fact only -the part originating from the (nonperturbative) minimization in the 2,'s of -the S-modes. -As stressed in ref. (8) there is another part whose origin lies beyond our -approximation, involving the consideration of 4th-order monomials in both -transverse and longitudinal field modes. -The issue we want to address ourselves to in this section is thus to find out -whether the logarithmic corrections to (4.1), induced by the interaction among -U- and S-modes, could modify the conclusions reached in the preceding section -about the essential instability of the perturbative Yang-Mills vacuum. As -already noted, there is a direct route to answer this crucial question, which -is barred by considerable, if not unsurmountable, difficulties. -ttowever, as we shall now see, all such labor can be saved at once by making -use of a general argument, which will demonstrate that the renormalization -of (4.1) does not alter our conclusions. -In order to accomplish our task, we shall carry out an analysis of the -coupling between S- and U-modes that is perturbative in character (*). -That this way of proceeding is a sensible one has already been indicated -by the previous variational calculation, where we have noted the close paral- -lelism with perturbation theory, which shows that the problem of the renor- -realization of the U-modes by the S-modes is perturbative (in the S-modes) in -character. Perturbative character which obviously is not shared by the whole -problem studied in this paper. -Thus separating the S- from the U-modes -(4.2) A,,(x) = n,,~(x) + V,,~,(x) +/,,(x), -(*) We show in appendix F that in a simplified example (~4 with negative renormalized -mass squared) the result we are about to prove holds in the variational framework of -sect. 3. - - -=== PAGE BREAK === - -(4.5) -(4.6) -and (*) -ESSENTIAL QUANTUM 1NSTABILIT~ :ETC. -and fixing the (( background gauge ~) -(4.3) D~(] § ~) ~/~s(x) ~- 0, -we define the S-modes, partition function Z -(4.4) Z~ =f[dv~ ] H ~(D(/+ ~o)V~)AInu] exp [iS'], -x -where the action is defined as (S(A) being the Yang-Mills action) -S'= S(A)- S~,, -(4.7) ~$~(x) = -- ~J(O- ),,(x, y) ~U,~(x) ~U~,'(x~) ~/~(x~) U"~"('~'~)U"~('+~) ; -379 -0 -1 is the inverse of the operator defined in (2.12). -Finally A[~/B ] in (4.4) is the Faddeev-Popov determinant, appropriate to -the (( background gauge ~) (4.3). -Our problem is then to compute the renormalization of the effective Hamil- -tonian operator in the space of U-modes, //c.) It is clear that calling 0~(x) ~eff ~ -the stress-energy tensor relative to the action --- ~(A) - ~(! § v~) + s(! § v~§ ~), -~'o'- 1/z~f[dn.] I] ~(~v~] ~[n~]fd'x0oo(., 0)oxp [iS'] eff -- -(4.8) -one has -eqs. (4.8) generate an infinite set of Foynman diagrams. However, for our -purpose---the calculation of O(g ~ In A~/gH) corrections to (4.1)--we need oMy -\ / -11 \% / ,, -a) b) -Fig. 3. - Coefficient of a) the quadratic and b) quartic parts of ==,,,~1~) (eq. (4.6)). -(*) The field ~a is precisely what reproduces, once inserted in the action S, the third -diagram of fig. 2. - - -=== PAGE BREAK === - -380 G. PREPARATA -consider the one-loop contributions to the coefficients of the quadratic and -quartic (in ~) parts of H(~)~ (see fig. 3). -Beside the operator 17r it is useful to consider the analogous coefficients ~eff -of the full Hamilton]an operator H (~), defined by changing in (4A) S' with S(A). -Let us consider the coefficient of the quadratic part first (fig. 3a)). To one -loop it coincides with the coefficient of H (~). In view of the conservation prop- -erties of 0~(x) and of the gauge we work in (*), we can write the diagrammatic -equation -| 3 ~(2) -f (4.9) ..... 2~ d ~Ooo(/ + ,j.), -where ~(~) O~,,(A) is the quadratic part of the stress-energy tensor and to -O(g 2 In A2/gH) we have (s) -(4.1o) I/Zs-= 1 -- ll/24z~g ~ In (A~/gH). -Equations (4.5) and (4.18) imply that the renormalization of the quadratic -part of the effective ttamiltonian can be effectively compensated by a corre- -sponding renormalization of the wave function of the U-mode. Indeed com- -puting now the expectation value of H (=) on the U-modes Gaussian state, we elf -have for the renormalized u-term E(~). -(4.11) E (~ H2/2uR H212u(1 11124~2g 2 In (A~/gH)) -Let us now turn to the coefficient in fig. 3b). Again its renormalization prop- -erties shall be inferred from those of the full Hamiltonian operator H ~). It -is only necessary to draw all the diagrams contributing to both coefficients -up to one loop to realize at once that the two classes coincide, but for the set -reported in fig. 4, which represents the insertion of the stress-energy tensor on -the external U-modes. Indeed these diagrams contribute to the full Hamil- -tonian H~-) but not to H(e~)~. -\\ 000 I 0 9 "~r // "~ / / -"s, + ... 4- 5 ( -/ \ / ~, -/ \ / \ -/ \ / ~, -4-... -Fig. 4. - Diagrams contributing to H (u) but not to ~eft,rr(~)" the dashed lines represent -the U-modes, while the continuous lines represent the S-modes. -(*) In the background gauge there is only one renormalization constant (see, for in- -stance, ref. (s)). -(s) L.F. ABBOTT: Nucl. Phys. B, 185, 189 (1981). - - -=== PAGE BREAK === - -ESSENTIAL QUANTUM INSTABILITY ETC. 381 -A straightforward calculation shows that the diagrams in fig. 4 give pre- -cisely the same contribution as those without insertions. At this point our task -is almost completed, for we know that the coefficient of the quartic part of -H (~) is also multiphcatively renormMized by 1/Z~ (cq. (4.6)) (*). -Thus we many write diagrammatically (to one loop) -% / -I <1 ~) ,, ,, ,§ ,/ ", ," ",+Ooo ,,, 1 x / - Xvj ~ / -(4.12) = ~ /,% + ,~ +...+ + < + > +... = -~'~X'"" "" +" ] 2 + x) 9 __ (' -Z8 /J % \ /" ~% -/ 9 / % -Thus we have -(4.~3) = + / %\ // -/ ~, / u / \ / -[ " "1 ~'~,% /// \% / / -= (2-1) ,, + > ,< -Z B / \ // \~ * // ', / % -Taking the expectation value of (4.11) on the Gaussian state for U-modes, -we obtain for the renormalized u-term E (~> --OR -24~r~ g 2 4 \ZB ] 2 4 1--2-- ~in ~' -H~ u2 / 11 A~ ~ -"~ 1 -- -- g21n , -For the complete renormalized contribution we obtain -(4.15) -whore -(4.16) us= u(1- 11124=~g= In (A=IgH)). -By comparing (4.15) with (4.1) we see that the only effect of renormalization -is to change u to ua (eq. (4.14)), which has obviously no consequence upon -the minimization of the energy density. -t*) This is a consequence of the renormalizabflity of the Yang-Mills theory. - - -=== PAGE BREAK === - -382 G. P~EPARATA -Thus the essential instability of the perturbative vacuum induced by the -nonperturbative U-modes' amplitudes is not removed by the renormalization -due to the coupling of the U-modes to the S-modes. -One should notice that (4.16), apart from the coefficients of the u~-term -and of in (A2/gH) in (4.16), is totally consistent with the conclusions of rcf. (3). -Furthermore, the origin of the different factors appearing in (4.12) and (4.13) -can be traced to the circumstance that the renormalization of the uS-term -receives contributions from both the magnetic and the electric parts of the -Hamiltonian, while the lowest-order contribution originates from the magnetic -term only. -We conclude this section by recalling that the (~ no~renormalization ~) result -that we have just obtained is physically quite transparent and, so to say, -inevitable. Had we indeed found a logarithmic renormalization of the lowest- -order contribution of the U-modes to the energy density (--H~/2), this would -have meant that~ upon measuring the energy density of field modes that are -completely insensitive to the ultraviolet cut-off~ such as the U-modes~ one -could nevertheless discover the existence of the cut-off. -5. - Conclusions. -The original aim of this paper was to fill the gaps left by the discussion -in ref. (s), by means of an improved variational ansatz, which could simulate -some of the important features of the porturbative coupling between S- and -U-modes. In the course of the analysis described in sect. 3 we have discovered -the existence of the term (3.14), which makes the conclusions of ref. (3) even -more drastic. Indeed our central result (eq. (3.17)) for the difference between -the energy density of our state and the perturbative vacuum: -(5.1) E(H)- E(O) ------ 11/48~2g~H ~ in (A2/gH) ~- O(g2H ~) -implies a local minimum -(5.2) gH*= aA ~ -and the energy difference at the minimum -(5.3) E(H*)- E(O) =- bA 4 , -where a and b (a, b > O) remain finite when g -* 0. -What does all this mean? The answer is very simple: there exist Savvidy -states of the gauge field, characterized by a chromomagnetic field H* in a - - -=== PAGE BREAK === - -ESSENTI&L QUANTUM INSTABILITY ETC. 383 -fixed direction in both space and colour space, whose energy density is, ac- -cording to (5.1) and (5.3), infinitely lower (when A -+ ~) than the perturbative -ground state. -A~d, if we still believe that QCD is the best candidate for a theory of the -strong interactions, we have no other choice but to abandon altogether pertur- -bation theory and look, may be along the directions open by this work, for the -real QCD ground state. For one thing we know from the variational nature -of our calculation: the energy of the real ground state must be equal or lower -than (5.1). We have also seen that, due to the peculiar dynamical behaviour -of the U-modes, there is a definite advantage to (i switch on ~> in the classical -vacuum a constant chromomagnetic field H*. This makes it plausible that -the real QCD ground state should be not too far from the one we have dis- -cussed here. -Finally a brief comment on the results of sect. 4. According to them (and -the discussion in appendix F) we have now a full proof that the coupkng of -the U-modes to the S-modes does not change in any fundamental way the -(, classical ~> dynamics of the U-modes. This fact, whose physical soundness -as well as theoretical origin were clearly spelled out in ref. (a), has been the -subject of a rather pointed controversy (4). Xu ref. (4) it has been suggested -that the renormalization of the U-modes induced by the S-modes should tame -the instabilities caused by the U-modes~ and reinstate the validity of perturba- -tion theory at short distances. :Not only does this circumstance seem hardly -believabl% but according to our proof it is just incorrect. -I wish to thank most warmly M. CONSOLI for collaboration in the initial -stage of this work and for many enlightening discussions. I also wish to -thank S. TAZZARI~ Director of Laboratori Nazionali di Frascati of INFN, for -his kind hospitality at Frascati, where part of this work was carried out. -APPEbIDIX 2~. -We shall now give a derivation of eq. (2.9) together with an explicit expres- -sion for the Faddeev-Popov determinant A[U], associated to the gauge fixing -Following FADDEEV-POPOV (5), the problem we wish to solve is to extract from -the matrix elements of any gauge-invariant operator on gauge-invariant wave -functionals a universal (infinite) constant, that may therefore be ignored. - - -=== PAGE BREAK === - -384 ~. PREPARATA -Let us define the gauge-invariant functional -(A.2) AI[V] -' =f[dg(x)] 1FI a[](~)], -where ](~)----0 is a generic gauge fixing, ~9(x) belongs to the class of time- -independent gauge transformations, and -(A.3) ~(X) [~ = ~(~(X) ~k(X) ~(~--1 ~_ ] /g~k ~(~(X) ~t~--l(x) -is the fluctuation gauge transformed by tQ(x). -The most general matrix element -(A.4 ) = f [dv] w*[~l] O [v, -- i ~] ~[~l] -according to (A.2) can be written as -(A.5) - 9 ~[~]*o [~,-i ~] ~[~], -which, using the gauge invariance of AI[~/] , F[~], !p[~t] and 0[~,--i(8/~)], -can be east in the form -(A.6) --O -The above equation solves our problem, due to the constancy of Va =S [dK2(x)]. -From (A.2) we see that in order to evaluate zlf[~] we need only integrate -upon infinitesimal transformations K2(x) = (1 + o)(x)). -Thus we have -f f [ (A.7) A[~]-' = [dO]~(f(~")) = [d~,] I] ~ /(~) + ~ o~ = x -/ lF, -i.e. -ko~o/ - - -=== PAGE BREAK === - -ESSENTIAL QUANTUM INSTABILITY ETC. 3~5 -Setting now -aud recalling that -I(7) = D~(/)7~(~) , -(A.9) ~o$(y) -we finally obtain for 3[7], appearing in (2.9), the expression -(A.10) A[7 3 -~ det([DTr(/)D~'(/) + ge~TDf~'(/)7~(x)]~a(x--y)}. -Introducing, as usual, Grassmann variables c~(x) and ~(x) we may write -(neglecting irrelevant constant factors) -(A.~3) -where -(A.12) -and -(A.13) -A[73 =f[dc] [ae] exp [-{fa3 xe(x)(~)2)c(x)+gf43x d3 y ~(x)A(x, y)c(y)}], -A~(x, y) = g~a~DTa(x)7~(x) -(D,)~ (x, y) = Jg~(x) Jg~(x) ~(x-- y). -A simple c~flculation shows that to O(g 2) no ultraviolet divergences arise -proportional to the unstable-mode amplitude, thus justifying our neglect of -A[7 ] both in ref. (a) and throughout this paper. -Aeen~Dix B -The Gauss law constraint that we wish to solve is -(B.1) -Setting -(B.2) -and -(B.3) -(B.I) becomes -(B.4) -~o[~] = ~[7]F[7] -r[v] = e~p [w[7]], -~W -~0. - - -=== PAGE BREAK === - -386 o. P~VA~TA -Using the (~transversality)) D~~ ~ , y) = 0, we obtain -(]3.5) 8W _ f i ~'d~y 8W -Expanding W[V] as in (2.30) (B.5) takes the recursive form -(K6) -and (k>2) -(B.6') -8w ~) 3 f d~ Y a-;'a~( x, Y) v~(Y) -8WC~+k) 8W(~+k) -Dr(x) ~(x) - ~a~(x) 8~(x) ' -whose solutions can be easily written as -(B.7) w,~) = ~ 7a(x' y) d~vi(y) G ~"~(y, ~) v~,(~) dy dz -and for k>2 -(B.7') -where -(B.8) -with - 9 ,k,.,/ 8~fi(y) ' -1 qx/~ -(B.9) = D~ (x).D~ (x), -obeys the equation -(B.30) D;~(x) D~,~'(x, y) = ~(x-- y). -For our purposes eqs. (A.7) need no further development, for when the electric -part of the Hamiltonian is applied to the state (A.2), one obtains -(B.13) 1 8 2 1 -l~ 1 8 2 W -2 8~]7(x) 8~d(x) ~'[~] = ~ ~ "(x, x) -- 2 8~'(x) ~'(x) -1 ~,~ 8W .~_,~,~, 1 8W 8W - - -=== PAGE BREAK === - -ESSENTIAL QUANTUi~I INSTABILITY ETC. 387 -Keeping terms up to O(g~), and carrying out the Gaussian functional integra- -tion, we obtain -(8.12) 1 <~o] ~fd3xE~(x)]y~> = -geeoaeeo ~ Fd3y , 1 __ " 'j d3y _~ (y, y')e~'. -8 -oQ' y ) G ~r y') + y) ,wo',.. 9 ((~,(y, , -~' ~o'o,.., ~,~,,~, y')} + -terms independent of the propagators G. -In (]3.12) 6~(x, y) is the <, transverse ~) &function -(8.13) (}if(x, y) = ~ ~'(x)~-~o~(y),v, -where the functions ~o~z~(x) have been defined in (2.13) and (2.14). -APPENDIX 0 -We derive here the relevant formulae needed in the discussion in sect. 3. -2h-modes + ll-mode. We evaluate first (10> denotes the Gaussian wave -functional) -(C.1) E~ = ~ (Ola~:(y~)a~:(y2)b~(y)H2a~.:(x~)+a~.:(x2)+b~(x)+lO)" -: n2 f~flx~,fll., 0 flaottl'~" X ~ H O~a'l*, AI lzB,~y~ -where use has been made of the easily proven results -1 fr~-i aB /~ [H2, a~(x)+] = ~j~ is(x, y)%(y) (c.2) -and -(c.2') -etc. -We next compute -(C.3) E~ -- -[aT(x), a+~(y)] = HTf(x, y), -+ h.c. -~ ~ ..... /x x) = 9 5 KT:g/?(x~, x~, ..~,.. ~ ~, x~, , -XlX2X -26 - Il Nuovo Cimento A. - - -=== PAGE BREAK === - -388 o. ~REPARATA -where -(0.4) Kq,,, (xl, x2, ku,~, xl) ~ ii, ,-, x2)Lk,(z, x) q- -t~ -Dr~ L~u(z, x) ~" -{- ~,, ,~, x2)Lf['(z, x)) -~ a~ 00~ H]i ` (Z, Xl)H;7:(~ , X2) } 9 -Upon imposing the minimization equation -~A ..... (E~ fi- E~) = o, tli~i -(0.5) -one obtains -(C.6) A~.,, (x~, x~, -where Kl~:~)f is the symmetrized kernel (C.4). Introducing ((!.6) into E~ -~ E3 -one readily obtains (3.11). -21-model ~ Jh-mode. An identical procedure leads us to (3.13) in the text. -APPENDIX D -We shall now show that quadratic divergences to O(g 2) are absent from -the sum of the contributions (2.11) and (3.11). In calculating the quadratic -divergent pieces we shall employ the leading behaviour of the propagator -H~f(x, y), -( 3 21pl exp lip(x-y)] a,- . -Inserting (D.1) into eq. (2.11), we get -2 dp 1 1 -(D.2) (2.11) ~gg~ (:~r) 3- IPl r "(x'x)d3x+ -~ g~3 ( a Ipl ~j~(x, x) dax-~ logarithmic terms, -while from eq. (3.11) we obtain after some simple algebra -(3.11)=__g,/3/'da~t_~ 1 1 /" (D.3) ~JL~"~(x, x)dax + logarithmic terms. -tpl -Putting (D.2) and (D.3) together one obtains the ammuneed ,ncellation. - - -=== PAGE BREAK === - -ESSENTIAL QUANTUM INSTABILITY :ETC. 389 -~ext we prove that E~ 8~ gives ~ term --H2/2 u2/4 to the energy density. -Upon specializing (3.13) to the U-modes, i.v. setting s y)= UT](x, y), -and taking into account that (within irrelevant terms ---- O(ps)) -(]).4} -one obtains -U~l~ (x, y) ~ 0 -[.-f (]).,~) .E'~"_ ~-g,/2 ~ 2-~-}J ' --.r -recalling that u = (g2/4~2) ~/~(dp/~(p)), one rewrites (D.5) as --~/y~ -(]).5') -which is the desired result. -H 2 u 2 -2 4' -APPENDIX ]~ -in this appendix we shall show that in the (classical) limit g-> 0, the -U-modes build up a solitonlike solution. -Let us write the gauge field projection on the U-mode -(E.1) {~')@I~,~ = ~:L,-( -),,, -n -where the spatial part for the  mode is given by -(E.2) ~n(x~) = exp :~ i --Tny exp -- x-- ~--::T~ n . -As we are interested in the limit g --> 0, we can choose the following quantiza- -tion volume (with periodic boundary conditions): -95 $~ -I:~:1, lYI
  • > (gH)--~ -so that when g --> 0 both L and L~ go to c~. in such a quantization volume -the only mode that survives in (E.2) is the one with n ---- 0, and (E.1) becomes -1 -(E.3) ~<,">?,(x) ~ Z ~_+(z, t) sG. - - -=== PAGE BREAK === - -390 O. PR~PARATA -A simple calculation gives for the action -(E.4) S ~--f4zdt{cb+(z,t)~--3~cf+(z, rP §247 -§ (§ -+ --) --Z~ [m+(z, t)qJ_(z, t)], , -where we have chosen the gauge so as to muke ~s_+ real. -The classical Euler-Lagrange equations are therefore -(~.5) -g2 -~+(z, t) -- 3**q~+(z, t) -- gHq~+(z, t) § 2 -~ q~+(z, t)q~_(z, t) 2 = O, -g~ -~_(z, t) -- ~_(z, t)- g~q~ (z, t) + 2 -~ ~_(z, t)~+(z, tp = o, -which admit a solution ~s+----~_--~ ~s such that -2g~ ~3 = 0 . (E.5') ~ -- ~ -- gH~ + --~ -The solutions of the two-dimensionM equation (E.5')are well known, in -particular the static solutions are -(E.6) -We can now compute the energy. One has -(E.7) E = ~(z, 0)5 § ~(z, 0) 2- gHq~(z, 0) 2 § -~ q~(z, 0)4 = -Zz/s -(gHpL~ z tgh z ~----V 4g 2 4 ' ---Lzl~ -which coincides with (2.20). -Our derivation shows that as fur as the classical part of the energy density -is concerned all the physics does come from the U-sector, even though, strictly -speaking, (E.1) are not solutions of the classical field equations, as pointed -out in appendix (A.3) of ref. (4). -APPENDIX F -In this appendix we will anMyse the origin of the (( nonrenormMizution -theorem ~), discussed in sect. 4, in the simple ),F4-theory. - - -=== PAGE BREAK === - -ESSENTIAL QUANTUM INSTABILITY ]~TC. 391 -In analogy with our problem w,3 shall consider a Lagrangian with negative -(renormalized) squared mass: -~e = 1/2 (~.~)~-- U(~) (F.1) -with -2 (F.2) u(q) = -4- 1/2 ~' -4- ~ ~', -where #~ is assumed to generate a negative renormalized mass, i.e. we set -(F.3) #~ = _#3 -4- A S ~ e. ~t-, -n -where #~ is a finite positive number and the coefficients c,, are suitably chosen -so as to cancel the quadratic divergences of perturbation theory. Note that -in gauge theories such a cancellation holds automatically. Quantizing the theory -in the symmetrical phase (q> ~ 0, we decompose ~v according to -(F.4) ~ = ~Vs -4- ~v , -where ~v(~s) refer to an eigenmode expansion with momentum Ip] #), likewise for the propagator G(x, y) we have -G(x, y) = G~(x, y) -4- G~(x, y) -f d3p 1 G~(x, y) ---- (2~r) 3 22u(p) exp [ip(x--y)], IpI<~t -f d3p 1 (~F.5") Gs(X' Y) : (2Y~) a 22s(p) exp [ip(x--y)], -computing the energy density on the Gaussian functional, we readily obtain -(F.6) E 1 1 = ~ [~l(x, x) -4- G~l(x, x)] ,§ 08[~s(x, x) -4- G~(x, x)] -4- -2 2 -4- ~ G~(x, x) G~(x, x) -4- ~ [~(x, x) G~,(x, x) -4- Gs(x, x) G~(x, x)] -with 0~ = (-- V ~ -4- #I). Setting -2 f d3p 1 #~ (F.7) /~ -4- ~ (2~) s ~s(p) -- -Ipl~># -(F.5) -with -(~..5') - - -=== PAGE BREAK === - -392 z. rRSPARATA -and minimizing in 2s we obtain the contribution of the S-modes -(F.8) -where -(F.9) -'~1 f , --~dap E~ = ~ Vp~- #~ + ~/:~ ~ .... + -tpl~.u -_}_#_2 ~ In ----u~ln 2 32~ ~ 256~ ~ ' -U = (1~(x, x) =f d3p ] -Ipl<# -Summing to (F.8) the contribution of the U-modes, we obtain -(F.]0) E--_~--~-~u 1-- 2 ln~q ~-gu 1-- -which shows that the variational Gaussian approximation produces not only -terms of O(~u In (A~/#2)) but also terms O(),~u 2 In (A~/#~)), which in a perturba- -rive expansion arise only at the 3-1oop level, ttowever, the terms we obtain do -not exhaust such a contribution. Indeed we can improve our Gaussian state -IG> in the way suggested in sect. 3. We treat the S-modes perturbatively -(i.e. we set ~Jp)= ~/p2 #3) and the contribution of the U-modes in the -Gaussian approximation (without minimization in the S-modes) is -(F.n) E0~-- u 1-- ln--: + uS. g -We improve the Gaussian ansatz as -(F.12) I~> = (~ + 26u)) (;, -where -1 1 t (F.13) 6(41- 7-= IA(Xl, -V~ v2 ! J -x2; yx, Y2) sr sr ur ut(y2), -and st and u+ are the creation operators for S- and U-modes, respectively. -Calculating the S-mode quadratic Hamiltonian (*) and the full quartie t~amil- -tonian on (F. 12) up to Q(~2) and minimizing with respect to the amplitudes A, -we obtain the extra contribution -(F.14) E(,) = -- 4V X--~-~ fG](x, y) G~(x, y) G~(x, y) G~(x, y), -xy -(') Note that we are now treating the S-modes perturbatively, just as in the proof -of our nonrenormalization theorem in sect. 4. - - -=== PAGE BREAK === - -ESSENTIAL qUANTUM INSTABILITY ETC. -which modifies (F.11) as -(~.15) /22 A2 )' u 2 -- ~ In Et'--~ 2 u 1-- In +~ -32~ ~ # 5/+ ~ u s 1-- = _ -393 -@2 R~ -which has the same structure of eq. (4.15). -The minimum of (F.15) coincides with the lowest-order value E* = --#4/22. - 9 RIASSUNTO -Si dimostra l'esistenza di configurazioni dei eampi di gauge la cui densit~ di energia -inferiore a quella del vuoto perturbativo di Yang-Mills di una quantit~ ehe diverge -come A 4 (A ~ il taglio ultravioletto). A questa singolare situazione fisica, che impedisee -l'uso delia teoria perturbativa anche a piceolissime distanze, b stato dato il home di -(~ instabilit~ essenziale ~. -PO3IOMe rle rlo.rty,-lOHO. diff --git a/proposals/P229-preparata-qcd-vacuum-audit/sources/preparata1986-nuovo-cim-a96-366.pdf b/proposals/P229-preparata-qcd-vacuum-audit/sources/preparata1986-nuovo-cim-a96-366.pdf deleted file mode 100644 index c8387f20..00000000 Binary files a/proposals/P229-preparata-qcd-vacuum-audit/sources/preparata1986-nuovo-cim-a96-366.pdf and /dev/null differ diff --git a/tests/test_public_contribution_surfaces.py b/tests/test_public_contribution_surfaces.py index dc2a17d2..008540f2 100644 --- a/tests/test_public_contribution_surfaces.py +++ b/tests/test_public_contribution_surfaces.py @@ -117,3 +117,25 @@ def test_contribution_policy_blocks_sensitive_and_unlicensed_sources() -> None: assert "paywalled" in contributing assert "redistribution" in contributing assert "must not merge" in contributing + + +def test_rights_restricted_preparata_sources_are_not_distributed() -> None: + source_directory = ( + ROOT / "proposals/P229-preparata-qcd-vacuum-audit/sources" + ) + restricted = ( + "preparata1986-nuovo-cim-a96-366.pdf", + "preparata1986-extracted.txt", + ) + for name in restricted: + assert not (source_directory / name).exists() + + ignore_rules = (ROOT / ".gitignore").read_text(encoding="utf-8") + for name in restricted: + path = f"/proposals/P229-preparata-qcd-vacuum-audit/sources/{name}" + assert path in ignore_rules + + source_notice = (source_directory / "README.md").read_text(encoding="utf-8") + assert "10.1007/BF02833896" in source_notice + assert "d712d4a085582ac390701e0a1f43bf21796f0971eda9f355c48da8b0d98b5b8a" in source_notice + assert "2cb0a6ca8b929d3e1513a27351173cbe05b354c1bcbc878ccaee77092c2dc961" in source_notice