The Equivalence Theorem at work: manifestly gauge-invariant Abelian Higgs model physics

Bram Boeykens; David Dudal; Thomas Oosthuyse

REVIEW 3 major objections 5 minor 1 cited by

The Equivalence Theorem at work: manifestly gauge-invariant Abelian Higgs model physics

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The Abelian Higgs model can be rewritten in gauge-invariant fields without losing renormalizability.

desk verdict A promising proof-of-principle for FMS variables as elementary fields, but the decoupling of gauge-fixing remnants is argued too quickly and needs a proper proof. read the letter →

arxiv 2412.10172 v2 pith:2VSEI4NW submitted 2024-12-13 hep-th hep-ph

Bram Boeykens , David Dudal , Thomas Oosthuyse This is my paper · ORCID

classification hep-thhep-ph PACS 11.15.-q11.10.Gh

keywords EquivalenceTheoremextendedBRSTsymmetryAbelianHiggsmodelFrohlich-Morchio-Strocchioperatorsgauge-invariantcompositerenormalizabilityNielsenidentityperturbationtheory

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that the Abelian Higgs model can be rewritten entirely in terms of gauge-invariant composite fields, the Fröhlich–Morchio–Strocchi operators $O = \phi^\dagger \phi - v^2/2$ and $V_\mu = -i \phi^\dagger D_\mu \phi$, as if they were elementary. Even though the resulting action contains infinitely many vertices and looks nonrenormalizable by power counting, the paper claims it is in fact renormalizable. The reason is the Equivalence Theorem in an extended BRST form: physical correlation functions of the gauge-invariant operators are unchanged by the field redefinition, so they inherit the finiteness of the original renormalizable model. If correct, this makes manifestly gauge-invariant perturbative Higgs computations possible diagram by diagram, avoiding gauge-variant fields and their unphysical spectral properties.

What carries the argument

The load-bearing mechanism is the extended BRST symmetry used to prove the Equivalence Theorem. A fictitious parameter $\alpha$ interpolates between the original and transformed fields; the BRST variation makes $\alpha$ appear only in a $\delta$-exact term, and a Slavnov-Taylor identity yields a Nielsen identity stating that correlation functions of the physical operators are independent of $\alpha$. The admissible transformations are restricted to those mapping the original fields to renormalizable composite operators, here the FMS operators $O$ and $V_\mu$. The argument then uses two decoupling steps: constant ghost propagators from the Jacobians produce dimensionally regularized loop integrals that vanish, and the remnants of the Landau gauge fixing are argued not to affect physical correlation functions. The final action is the classical action in terms of $O$ and $V_\mu$, with counterterms transformed from the most general counterterm structure of the original model.

What would settle it

Compute the one-loop two-point function of $O$ from the full gauge-fixed reformulation, retaining the $b$–$\rho'$ propagator listed in the paper's Eq. (38) and the $\rho'$ remnants, and compare it with Eq. (41). If any nonvanishing contribution survives or a divergence not canceled by the counterterms in Eq. (33) appears, the decoupling of the gauge-fixing remnants is wrong and the simplified action is incomplete.

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Extended reading notes

Core claim

The central discovery is that the classical Abelian Higgs action, written in terms of gauge-variant fields, can be recast as an action whose elementary fields are the gauge-invariant FMS operators $O$ and $V_\mu$. The re-expression is an admissible field transformation in the sense of the paper's extended-BRST version of the Equivalence Theorem: it is a local, invertible change of variables of the form $\phi \to \hat{\phi} + \hat{\phi}^2 g(\hat{\phi})$, and the operators in question are renormalizable composites in the original theory. The transformed action has infinitely many vertices and a Proca-type propagator for $V_\mu$, which would normally signal nonrenormalizability, but the theorem guarantees that correlation functions of $O$ and $V_\mu$ coincide with those of the original formulation. The paper verifies this at one loop for the $O$-propagator, obtaining exactly the finite result previously found with the original fields; all divergences cancel when the counterterms inherited from the original model are used.

Load-bearing premise

The whole simplification rests on the assumption that the extra fields introduced by the gauge fixing and the change of variables—the ghosts and the auxiliary b-field—never contribute to physical correlation functions of the gauge-invariant fields, even though one of those auxiliary fields has a nonzero propagator with the leftover radial field $\rho'$.

Editorial extensions

If this is right

Perturbative computations of physical Higgs observables can be performed in terms of gauge-invariant fields order by order, with no gauge fixing needed at intermediate steps.
The one-loop gauge-invariant scalar two-point function and its pole mass reproduce the earlier composite-operator result computed in the original variables, providing a concrete check of the equivalence.
Although the gauge-invariant action has infinitely many vertices, only the finite set of counterterm parameters of the original Abelian Higgs model is needed to render correlation functions finite.
The same extended-BRST Equivalence Theorem strategy can be applied to non-Abelian gauge-Higgs systems, leading toward fully gauge-invariant electroweak calculations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editor's extension: a direct check of the decoupling step would be to compute the one-loop $O$-propagator with the $b$–$\rho'$ sector kept, since the paper's Eq. (38) lists a nonzero $b$–$\rho'$ propagator, and verify that its contribution vanishes identically.
Editor's extension: the same logic implies a practical criterion for candidate gauge-invariant variables: if an operator is not renormalizable in the original variables, its correlation functions will depend on the interpolation parameter and the transformed theory will not be predictive.
Editor's extension: the framework invites a comparison of gauge-invariant versus gauge-fixed resummations of the Higgs propagator beyond one loop, which could quantify how much the unphysical spectral features of the gauge-variant fields affect pole-mass extractions.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's the short version: this is a genuinely interesting proof-of-principle for promoting FMS composite operators to elementary fields in the Abelian Higgs model, and the one-loop check is solid. But the central claim that the gauge-fixing remnants decouple is under-argued, and the argument in Section III C 5 misses the b-rho' mixing.

The new thing is the extended-BRST version of the Equivalence Theorem, used to rewrite the action in terms of O and V_mu. That combination is new, and the action (31) with its infinite vertex tower is written down explicitly. The one-loop O-propagator calculation in Section IV is careful; the agreement with Eq. (2.32) of ref. [38] is a genuine consistency check. The appendices (tadpole cancellation, effective action minimization) show care. The reliance on prior work [9,35,38] for renormalizability and counterterms is heavy, but those are published results, so that is not itself a flaw.

The soft spot is in Section III C 5. The authors argue the remnant gauge-fixing term (37) can be dropped because the b-b propagator is zero and rho' has no interaction vertices. That is only a tree-level statement. There is a nonzero b-rho' mixing propagator in Eq. (38), and the bVOn vertices are real interactions, so the effective b-b propagator can receive loop contributions, and b can enter the rho' sector. The paper does not give a BRST/Ward argument, an explicit computation, or a constant-propagator argument to show these contributions vanish. Without that, the simplified action (31) may omit terms, and the one-loop O-propagator (41) could be incomplete. I checked the one-loop diagram list in Appendix D; there are no b-line diagrams, so the gap is not addressed.

Is this fatal? Not necessarily. The equivalence-theorem machinery is plausible, and the original model's BRST structure suggests the decoupling should hold. But "plausible" is not a proof, and this gap sits exactly on the paper's main renormalizability claim. A serious referee should require a proper demonstration—probably via the BRST-exactness of the gauge-fixing term or an explicit check that b-insertions into physical correlators vanish.

Who this is for: people working on the FMS program, gauge-invariant Higgs physics, and algebraic renormalization. It deserves peer review, but it should not be accepted as-is. I would not cite the central claim until the decoupling is closed. Bring it to the reading group, maybe.

Referee Report

3 major / 5 minor

Summary. The paper develops an algebraic version of the Equivalence Theorem based on an extended BRST symmetry, and uses it to rewrite the Abelian Higgs model in terms of the gauge-invariant FMS operators O and V_mu as elementary fields. The resulting action (31) has infinitely many vertices and is not power-counting renormalizable, but the authors argue that physical correlation functions coincide with those of the original renormalizable model, so renormalizability is inherited. They further argue that the Jacobian ghosts and the remnants of the Landau gauge fixing decouple from physical correlators, leaving a simplified 'ungauged' action. As an illustration, they compute the one-loop O-propagator, Eqs. (41)-(43), and find exact agreement with the composite-operator result of ref. [38].

Significance. If the central equivalence and decoupling claims are fully established, this would provide a manifestly gauge-invariant perturbative framework for Higgs physics, with genuine practical value: correlation functions of the physical FMS operators could be computed directly in terms of O and V_mu, avoiding gauge-dependent intermediate quantities. The paper contains several strengths: a self-contained BRST derivation of the Equivalence Theorem, an explicit construction of the transformed action and counterterm structure, and a detailed one-loop O-propagator calculation whose agreement with [38] is a nontrivial consistency check. The main weakness is that the decoupling of the gauge-fixing sector is argued only at tree level, and the propagator list in Eq. (38) contains an internal inconsistency that obscures the argument. These issues are local and potentially fixable, but they are load-bearing for the central renormalizability claim.

major comments (3)

[III C 5, Eqs. (37)-(38)] The argument that bVOn vertices cannot contribute because the bb-propagator vanishes is only a tree-level statement. Two bVO or bVOO vertices connected by internal V and O propagators generate a one-loop b-b self-energy; the paper does not compute this self-energy or prove it vanishes. If the loop-corrected b-b propagator is nonzero, b-lines can connect bVOn vertices to one another and contribute to correlators of O and V, meaning the simplified action (31) would omit genuine contributions. The paper needs either an explicit all-orders proof, a BRST/Slavnov-Taylor identity argument, or a computation showing that such diagrams cancel or vanish.
[III C 5, Eq. (38)] The propagator list is internally inconsistent: it states Delta_{rho' rho'} = 1/(p^2 v^2), which implies a nonzero rho' kinetic term, but the action (31) together with the gauge-fixing term (37) contains no rho' kinetic term after the polar transformation—the Goldstone mode has been absorbed into the massive vector. Either Delta_{rho' rho'} is actually zero, in which case the list should be corrected and the decoupling argument should explicitly state that the nonzero b-rho' mixing propagator cannot appear as an internal line in physical correlators because no rho' vertex exists, or a rho' kinetic term must be identified and its contributions analyzed. As written, the inconsistency makes the decoupling argument in III C 5 hard to assess.
[IV, Eq. (41)] The one-loop O-propagator computation is presented as evidence for the equivalence, but it does not test the decoupling of the b-sector: b-contributions to <O O> first appear at higher loop order (a one-loop b-b self-energy insertion requires at least two additional bVOn vertices and hence a two-loop diagram). Agreement with [38] is therefore a necessary but not sufficient check of the central renormalizability claim. The paper should clarify that the explicit illustration is not a substitute for a proof that the b-sector decouples at all orders.

minor comments (5)

[Eq. (38)] The ghost propagator line reads 'Delta_{bar c c} = Delta_{bar c c} = -1/p^2'; presumably this should be Delta_{bar c c} = Delta_{c bar c} = -1/p^2.
[Eq. (43)] The logarithms in the first two lines are missing parentheses: they should read log((p^2 x(1-x)+m_h^2)/mu^2) and log((p^2 x(1-x)+m_A^2)/mu^2).
[Reference [30]] The reference is mistyped: it should be J. Goldstone, A. Salam, and S. Weinberg.
[III C 4, Eq. (35)] The decoupling argument in III C 2 is presented for a single ghost species with vertices of the form bar eta eta F. The second ghost sector in Eq. (35) contains mixed vertices such as bar omega V_mu omega_mu, so the extension of the constant-propagator argument to this mixed case should be stated explicitly; as written, the reader must infer that any closed ghost loop still yields an integral over a constant.
[III C 5, first paragraph] The sentence 'removal of the above gauge fixing terms will not influence the tree-level propagators of neither O nor V_mu' is grammatically confusing; 'neither ... nor' already carries negation, so 'will not influence ... neither O nor V_mu' should be rephrased, e.g., 'will influence neither the O nor the V_mu tree-level propagators'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the Equivalence Theorem is derived, the FMS transformation is explicit, and the one-loop O-propagator is a genuine computation rather than a fitted or definitionally forced result.

full rationale

The paper's derivation chain is not circular. Section II proves the Equivalence Theorem via an extended BRST symmetry and Nielsen identity, Eqs. (2)-(10); the theorem is derived, not assumed. The gauge-invariant action (31) is obtained by the explicit invertible transformation (28)-(29), and the one-loop O-propagator is computed from the Feynman rules of Appendix A and the counterterms (33), which are imported from the original-field renormalization [9,35] and are not tuned to the target correlation function. The equality with [38, (2.32)] is therefore a verification after the calculation, not an input: no parameter is fitted to the finite part of <O(p)O(-p)>, and no equation is used as its own input. The heavy reliance on self-group papers [9,35,38] for the renormalizability of the FMS operators and for the benchmark one-loop result is real external input from published work, not the output of this paper; under the review rules, such citations do not by themselves constitute circularity. The genuine technical weakness is the tree-level b-decoupling argument in Sec. III C 5, which overlooks the non-zero b-rho' propagator in Eq. (38) and possible loop-generated b-b self-energies; if that decoupling fails, the simplified action (31) would omit contributions and the loop result would be incomplete. This is a correctness risk, not a circularity, because the conclusion is not equivalent to its inputs by construction.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No data-fitting parameters are introduced; e, lambda, and v are the input couplings of the original model, and the counterterm coefficients are fixed by the renormalization scheme of refs. [9,35]. The fictitious parameter alpha in the Equivalence Theorem proof is a bookkeeping device and drops out of physical correlators. No new particles, forces, or conserved quantities are introduced. The extended BRST doublets and Jacobian ghosts are technical tools, not physical entities.

assumptions (4)

domain assumption The original Abelian Higgs model is perturbatively renormalizable and its most general counterterm action is the one determined in ref. [9].
Invoked in Section III C 3 to carry the counterterm basis over to the new variables (Eq. (32)). The present paper does not re-derive this basis.
domain assumption The composite FMS operators O and V_mu are renormalizable in the original field formulation, with the mixing patterns specified in refs. [9,35].
Used in Section III C to justify that the field transformation is admissible under the Equivalence Theorem. The paper relies on these prior results rather than proving them.
standard math Standard perturbative QFT machinery (path integral, Faddeev-Popov gauge fixing, BRST cohomology, dimensional regularization) is valid.
Used throughout Sections II and III to derive the Nielsen identity and to evaluate loop integrals.
ad hoc to paper The Jacobian ghost and gauge-fixing sectors decouple from physical correlation functions.
This is argued in Sections III C 2, III C 4, and III C 5. The argument for the b-field sector overlooks the nonzero b-rho' propagator in Eq. (38), so the decoupling is not fully established.

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Cite this review

Pith. "Pith review of The Equivalence Theorem at work: manifestly gauge-invariant Abelian Higgs model physics." pith.science (2026). https://pith.science/paper/2VSEI4NW

@misc{pith2026241210172,
  author       = {Pith},
  title        = {Pith review of: The Equivalence Theorem at work: manifestly gauge-invariant Abelian Higgs model physics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2VSEI4NW}},
  note         = {Machine review of arXiv:2412.10172}
}

read the original abstract

We reconsider the Equivalence Theorem from an algebraic viewpoint, using an extended BRST symmetry. This version of the Equivalence Theorem is then used to reexpress the Abelian Higgs model action, originally written in terms of undesirable gauge variant field excitations, in terms of gauge-invariant, physical variables, corresponding to the Fr\"ohlich-Morchio-Strocchi composite operators in the original field formulation. Although the ensuing action encompasses an infinite number of vertices and appears to be nonrenormalizable from the powercounting viewpoint, it nevertheless is renormalizable, thanks to the hidden equivalence with the original model. Hence, manifestly gauge-invariant computations are possible. We present an explicit illustration in terms of the gauge-invariant scalar field, its Green's function and corresponding pole mass.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Gauge-invariant Slavnov-Taylor Decomposition for Trilinear Vertices
hep-th 2025-06 conditional novelty 5.0 of 10

The paper extends the FMS sector-by-sector Slavnov-Taylor decomposition to trilinear vertices at one loop and tabulates ultraviolet divergent amplitudes that are claimed to satisfy the identities.

Reference graph

Works this paper leans on

52 extracted references · 37 canonical work pages · cited by 1 Pith paper

[38]

Goldstone, J

A. Goldstone, J. Salam and S. Weinberg, Phys. Rev. 127, 965 (1962)

work page 1962
[1]

(19) The change of variables is deﬁned as h = (h′ + v) cos ρ′ − v ρ = (h′ + v) sin ρ′ Aµ = A′ µ − 1 e ∂µρ′

Intermezzo: the non-admissible gauge-invariant polar p arametrization Following [9], we ﬁrst perform an intermediate change of variables to t he polar parametrization of the Abelian Higgs model, φ = 1√ 2 (v + h′)eiρ′ . (19) The change of variables is deﬁned as h = (h′ + v) cos ρ′ − v ρ = (h′ + v) sin ρ′ Aµ = A′ µ − 1 e ∂µρ′ . (20) 7 The Jacobian correspon...

work page
[2]

Decoupling of the polar ghosts from physical correlation functions We will now investigate the contributions from the ghost vertices to our theory, starting with the propagator as arising from (22), yielding the constant propagator ∆ ¯ηη = 1 v , (26) next to a single interaction vertex, ∫ d4x ¯ηηh ′. We will give the actual argument for ghost vertices of ...

work page
[3]

At last: admissible transformation to elementary FMS ope rators In III C, we have already formulated the Abelian Higgs model in a BRST invariant fashion, making use of the polar parametrization. To come to a renormalizable theory in terms of gau ge-invariant operators, we will now formulate the theory in terms of the renormalizable, composite FMS-operato ...

work page
[4]

∫ ddq (2π )d C /bracehtipupleft/bracehtipdownright/bracehtipdownleft/bracehtipupright = 0

The integration over this momentum will amount to the integration over a constant C, since the ghost propagator is a constant, moreover the ghost vertices will have as Feynman ru les −fi, also constants, such that we can write the contribution of each diagram with ghosts as, where the dots re present the other Feynman rules, propagators and integrations o...

work page
[5]

ungauged

Decoupling of the remnants of the gauge ﬁxing In the previous sections, we have obtained a theory written in term s of the excitations O, Vµ and ρ′, b, ¯c, c and ghost ﬁelds corresponding to the changes of variables. We will now a rgue why we can remove that gauge ﬁxing term from the ﬁnal action (31), to obtain an “ungauged” Higgs model. This is perhaps n...

work page
[6]

More decoupling ghost ﬁelds As before, there will be new ghosts arising from the Jacobian deter minant from the non-linear ﬁeld transformation (30). At the level of the action, this becomes via the introduction o f extra ghost ﬁelds (¯ω, ω ) and ( ω µ, ¯ω µ) Sghosts,2 = ∫ d4x [ ¯ω ¯ω µ ]   1 v 1√ 1+ 2O v2 0 − 4 ev4 Vµ 1 (1+ 2O v2 )2 δµν 2 ev2 1 1+ 2O v2...

work page
[7]

N. K. Nielsen, Nucl. Phys. B 101, 173 (1975)

work page 1975

Show all 52 references

[8]

augmented pe rturbation theory

We can infer that this is exactly equal to the expression found in [38, (2.32)] where this correlation function was computed in terms of the original (gauge variant ﬁeld variables). In particular, the counterterms (33) nicely cancel all divergences in the above two-point funct...
[9]

based on several constraining Ward identities–to the new variab les. C. Performing the change of variables
[10]

J. S. R. Chisholm, Nucl. Phys. 26, 469 (1961)

1961
[11]

Kamefuchi, L

S. Kamefuchi, L. O’Raifeartaigh, and A. Salam, Nucl. Phy s. 28, 529 (1961)

1961
[12]

M. C. Bergere and Y.-M. P. Lam, Phys. Rev. D 13, 3247 (1976)

1976
[13]

Blasi, N

A. Blasi, N. Maggiore, S. P. Sorella, and L. C. Q. Vilar, Ph ys. Rev. D 59, 121701 (1999), arXiv:hep-th/9812040

1999 arXiv
[14]

Ferrari, M

R. Ferrari, M. Picariello, and A. Quadri, JHEP 04, 033, arXiv:hep-th/0203200

arXiv
[15]

Cohen, M

T. Cohen, M. Forslund, and A. Helset, (2024), arXiv:2412 .12247 [hep-th]

2024
[16]

Piguet and K

O. Piguet and K. Sibold, Nucl. Phys. B 253, 517 (1985)

1985
[17]

Dudal, G

D. Dudal, G. Peruzzo, and S. P. Sorella, JHEP 10, 039, arXiv:2105.11011 [hep-th]

arXiv
[18]

Frohlich, G

J. Frohlich, G. Morchio, and F. Strocchi, Phys. Lett. B 97, 249 (1980)

1980
[19]

Frohlich, G

J. Frohlich, G. Morchio, and F. Strocchi, Nucl. Phys. B 190, 553 (1981)

1981
[20]

Maas, Prog

A. Maas, Prog. Part. Nucl. Phys. 106, 132 (2019), arXiv:1712.04721 [hep-ph]

2019 arXiv
[21]

’t Hooft, C

G. ’t Hooft, C. Itzykson, A. Jaﬀe, H. Lehmann, P. Mitter, I. Singer, and R. Stora, NATO Sci. Ser. B 59, 1 (1980). 17

1980
[22]

Piguet and S

O. Piguet and S. P. Sorella, Algebraic renormalization: Perturbative renormalizatio n, symmetries and anomalies , Vol. 28 (1995)

1995
[23]

Gomis and S

J. Gomis and S. Weinberg, Nucl. Phys. B 469, 473 (1996), arXiv:hep-th/9510087

1996 arXiv
[24]

Delduc, N

F. Delduc, N. Maggiore, O. Piguet, and S. Wolf, Phys. Let t. B 385, 132 (1996), arXiv:hep-th/9605158

1996 arXiv
[25]

A. Maas, R. Sondenheimer, and P. T¨ orek, Annals Phys. 402, 18 (2019), arXiv:1709.07477 [hep-ph]

2019 arXiv
[26]

Maas, in 57th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories (2023) arXiv:2305.07395 [hep-ph]

A. Maas, in 57th Rencontres de Moriond on Electroweak Interactions and Uniﬁed Theories (2023) arXiv:2305.07395 [hep-ph]

2023 arXiv
[27]

Sondenheimer, Phys

R. Sondenheimer, Phys. Rev. D 101, 056006 (2020), arXiv:1912.08680 [hep-th]

2020 arXiv
[28]

Maas and R

A. Maas and R. Sondenheimer, Phys. Rev. D 102, 113001 (2020), arXiv:2009.06671 [hep-ph]

2020 arXiv
[29]

Dobson, A

E. Dobson, A. Maas, and B. Riederer, Annals Phys. 457, 169404 (2023), arXiv:2211.05812 [hep-lat]

2023 arXiv
[30]

Binosi and A

D. Binosi and A. Quadri, Phys. Rev. D 106, 065022 (2022), arXiv:2206.00894 [hep-th]

2022 arXiv
[31]

Quadri, Theor

A. Quadri, Theor. Math. Phys. 217, 1879 (2023), arXiv:2311.18415 [hep-th]

2023 arXiv
[32]

Quadri, Eur

A. Quadri, Eur. Phys. J. C 84, 975 (2024), [Erratum: Eur.Phys.J.C 84, 1073 (2024)], arXi v:2402.01016 [hep-th]

2024 arXiv
[33]

Englert and R

F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964)

1964
[34]

P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964)

1964
[35]

P. W. Higgs, Phys. Lett. 12, 132 (1964)

1964
[36]

P. W. Higgs, Phys. Rev. 145, 1156 (1966)

1966
[37]

G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, Phys. Rev . Lett. 13, 585 (1964)

1964
[39]

Elitzur, Phys

S. Elitzur, Phys. Rev. D 12, 3978 (1975)

1975
[40]

Becchi, A

C. Becchi, A. Rouet, and R. Stora, Commun. Math. Phys. 42, 127 (1975)

1975
[41]

Kraus and K

E. Kraus and K. Sibold, Z. Phys. C 68, 331 (1995), arXiv:hep-th/9503140

1995 arXiv
[42]

Haussling and E

R. Haussling and E. Kraus, Z. Phys. C 75, 739 (1997), arXiv:hep-th/9608160

1997 arXiv
[43]

M. A. L. Capri, I. F. Justo, L. F. Palhares, G. Peruzzo, an d S. P. Sorella, Phys. Rev. D 102, 033003 (2020), arXiv:2007.01770 [hep-th]

2020 arXiv
[44]

Dudal, D

D. Dudal, D. M. van Egmond, M. S. Guimar˜ aes, O. Holanda, B. W. Mintz, L. F. Palhares, G. Peruzzo, and S. P. Sorella, Phys. Rev. D 100, 065009 (2019), arXiv:1905.10422 [hep-th]

2019 arXiv
[45]

Peskin and D

M. Peskin and D. Schroeder, An Introduction To Quantum Field Theory , Frontiers in Physics (Avalon Publishing, 1995)

1995
[46]

Dudal, D

D. Dudal, D. M. van Egmond, M. S. Guimaraes, O. Holanda, L . F. Palhares, G. Peruzzo, and S. P. Sorella, JHEP 02, 188, arXiv:1912.11390 [hep-th]

1912 arXiv
[47]

Dudal, D

D. Dudal, D. M. van Egmond, G. Peruzzo, and S. P. Sorella, Eur. Phys. J. C 83, 1091 (2023), arXiv:2309.16776 [hep-th]

2023 arXiv
[48]

Peruzzo, (2024), arXiv:2412.09406 [hep-th]

G. Peruzzo, (2024), arXiv:2412.09406 [hep-th]

2024
[49]

A. Maas, D. M. van Egmond, and S. Pl¨ atzer, in 42nd International Conference on High Energy Physics (2024) arXiv:2409.20131 [hep-ph]

2024 arXiv
[50]

Jenny, A

P. Jenny, A. Maas, and B. Riederer, Phys. Rev. D 105, 114513 (2022), arXiv:2204.02756 [hep-lat]

2022 arXiv
[51]

I. J. R. Aitchison and C. M. Fraser, Annals Phys. 156, 1 (1984)

1984
[52]

A. K. Das and J. Frenkel, Phys. Lett. B 726, 493 (2013), arXiv:1306.6307 [hep-th]

2013 arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [38]

Goldstone, J

A. Goldstone, J. Salam and S. Weinberg, Phys. Rev. 127, 965 (1962)

work page 1962

[2] [1]

(19) The change of variables is deﬁned as h = (h′ + v) cos ρ′ − v ρ = (h′ + v) sin ρ′ Aµ = A′ µ − 1 e ∂µρ′

Intermezzo: the non-admissible gauge-invariant polar p arametrization Following [9], we ﬁrst perform an intermediate change of variables to t he polar parametrization of the Abelian Higgs model, φ = 1√ 2 (v + h′)eiρ′ . (19) The change of variables is deﬁned as h = (h′ + v) cos ρ′ − v ρ = (h′ + v) sin ρ′ Aµ = A′ µ − 1 e ∂µρ′ . (20) 7 The Jacobian correspon...

work page

[3] [2]

Decoupling of the polar ghosts from physical correlation functions We will now investigate the contributions from the ghost vertices to our theory, starting with the propagator as arising from (22), yielding the constant propagator ∆ ¯ηη = 1 v , (26) next to a single interaction vertex, ∫ d4x ¯ηηh ′. We will give the actual argument for ghost vertices of ...

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[4] [3]

At last: admissible transformation to elementary FMS ope rators In III C, we have already formulated the Abelian Higgs model in a BRST invariant fashion, making use of the polar parametrization. To come to a renormalizable theory in terms of gau ge-invariant operators, we will now formulate the theory in terms of the renormalizable, composite FMS-operato ...

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[5] [4]

∫ ddq (2π )d C /bracehtipupleft/bracehtipdownright/bracehtipdownleft/bracehtipupright = 0

The integration over this momentum will amount to the integration over a constant C, since the ghost propagator is a constant, moreover the ghost vertices will have as Feynman ru les −fi, also constants, such that we can write the contribution of each diagram with ghosts as, where the dots re present the other Feynman rules, propagators and integrations o...

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[6] [5]

ungauged

Decoupling of the remnants of the gauge ﬁxing In the previous sections, we have obtained a theory written in term s of the excitations O, Vµ and ρ′, b, ¯c, c and ghost ﬁelds corresponding to the changes of variables. We will now a rgue why we can remove that gauge ﬁxing term from the ﬁnal action (31), to obtain an “ungauged” Higgs model. This is perhaps n...

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[7] [6]

More decoupling ghost ﬁelds As before, there will be new ghosts arising from the Jacobian deter minant from the non-linear ﬁeld transformation (30). At the level of the action, this becomes via the introduction o f extra ghost ﬁelds (¯ω, ω ) and ( ω µ, ¯ω µ) Sghosts,2 = ∫ d4x [ ¯ω ¯ω µ ]   1 v 1√ 1+ 2O v2 0 − 4 ev4 Vµ 1 (1+ 2O v2 )2 δµν 2 ev2 1 1+ 2O v2...

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[8] [7]

N. K. Nielsen, Nucl. Phys. B 101, 173 (1975)

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