On gauge invariance and spontaneous symmetry breaking

Aste, Andreas; Scharf, G.; Dütsch, Michael

doi:10.1088/0305-4470/30/16/019

Cited by 24 publications

(64 citation statements)

References 6 publications

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“…The local terms on the right-hand side of (4.3), which come from the causal splitting, are called "anomalies". The ordinary axial anomalies are of the same kind, they appear in the third order triangle diagrams with axial vector couplings to fermions (see [12], Sect.4). The difference is that the axial anomalies cannot be removed by finite renormalizations.…”

Section: Second Order Gauge Invariancementioning

confidence: 96%

General massive gauge theory

Scharf

1999

Nuov Cim A

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The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is used to construct massive gauge theories. We consider the interactions of r massive and s massless gauge fields together with (r + s) fermionic ghost and anti-ghost fields. First order gauge invariance requires the introduction of unphysical scalars (Goldstone bosons) and fixes their trilinear couplings. At second order additional physical scalars (Higgs fields) are necessary, their coupling is further restricted at third order. In case of one physical scalar all couplings are determined by gauge invariance, including the Higgs potential. For three massive and one massless gauge field the SU (2) × U (1) electroweak theory comes out as the unique solution.

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Section: Second Order Gauge Invariancementioning

confidence: 96%

General massive gauge theory

Scharf

1999

Nuov Cim A

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“…The τ 0 -equations express PGI-tree for the (ρ = 1)-theory, they have a unique solution for P 1 and P 2 given in (70) (cf. [ADS97,GB11]). …”

Section: Summary and Concluding Remarksmentioning

confidence: 99%

Massive vector bosons: Is the geometrical interpretation as a spontaneously broken gauge theory possible at all scales?

Dütsch

2015

Rev. Math. Phys.

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The usual derivation of the Lagrangian of a model for massive vector bosons, by spontaneous symmetry breaking of a gauge theory, implies that the prefactors of the various interaction terms are uniquely determined functions of the coupling constant(s) and the masses. Since, under the renormalization group (RG) flow, different interaction terms get different loop-corrections, it is uncertain, whether these functions remain fixed under this flow. We investigate this question for the U (1)-Higgs-model to 1-loop order in the framework of Epstein-Glaser renormalization. Our main result reads: choosing the renormalization mass scale(s) in a way corresponding to the minimal subtraction scheme, the geometrical interpretation as a spontaneously broken gauge theory gets lost under the RG-flow. This holds also for the clearly stronger property of BRST-invariance of the Lagrangian. On the other hand we prove that physical consistency, which is a weak form of BRST-invariance of the time-ordered products, is maintained under the RG-flow.

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“…In the CGI operator formulation of the BRST gauge formalism [9,10,19] there is a clear-cut distinction, whereas in the SLFT setting the idea of an SSB would not even arise since the matter fields which couple to sl vector mesons become themselves sl and hence do not comply with a physical picture of a global symmetry breaking in which the local current remains conserved but the global charge diverges.…”

Section: Introductory Remarks On Origin and Scope Of String Localizationmentioning

confidence: 99%

Beyond gauge theory: positivity and causal localization in the presence of vector mesons

Schroer¹

2016

Eur. Phys. J. C

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The Hilbert space formulation of interacting s = 1 vector-potentials stands is an interesting contrast with the point-local Krein space setting of gauge theory. Already in the absence of interactions the Wilson loop in a Hilbert space setting has a topological property which is missing in the gauge-theoretic description (Haag duality, Aharonov-Bohm effect); the conceptual differences increase in the presence of interactions. The Hilbert space positivity weakens the causal localization properties of interacting fields, which results in the replacement of the gauge-variant point-local matter fields in Krein space by string-local physical fields in Hilbert space. The gauge invariance of the perturbative S-matrix corresponds to its independence of the space-like string direction of its interpolating fields. In contrast to gauge theory, whose direct physical range is limited to a gauge-invariant perturbative S-matrix and local observables, its Hilbert space string-local counterpart is a full-fledged quantum field theory (QFT). The new setting reveals that the Lie structure of self-coupled vector mesons results from perturbative implementation of the causal localization principles of QFT. Introductory remarks on origin and scope of string localizationIt is well known that the use of point-local massless vector potentials is incompatible with the positivity of Hilbert space. One usually resolves this problem by abandoning the positivity requirement of quantum field theory (QFT) while maintaining the point-local field formalism which leads to gauge theory (GT). The price to pay is well known from quantum electrodynamics (QED) in the standard indefinite metric (Gupta-Bleuler) gauge setting: positivity can be recoveredDedicated to the memory of Raymond Stora and John Roberts.a e-mail: schroer@zedat.fu-berlin.de for local observables, whereas charge-carrying fields remain outside its physical range. The separation between physical and unphysical quantum fields is done in terms of gauge symmetry, which is not a physical symmetry but a formal device to extract a physical subtheory. Although the standard gauge formalism is restricted to the presence of vector potentials, the clash between zero mass point-local fields and positivity is a general phenomenon for all s ≥ 1 zero mass tensor potentials. It does not affect the corresponding field strengths, but the short-distance dimension of the latter (d sd = 2 for s = 1) prevents their direct use in renormalizable interactions.The alternative option is to accept the weaker localization required by positivity. The tightest covariant localization beyond point-local consistent with positivity turns out to be causal localization on semi-infinite space-like "strings" 1 x + R + e, e 2 = −1. It is easy to construct m > 0 covariant string-localized fields (x, e) in terms of semi-infinite line integrals on point-local fields [1]. The immediate advantage of such a construction is that one obtains two improvements in one stroke, the lowering of the short-distance dimension and the e...

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On gauge invariance and spontaneous symmetry breaking

Cited by 24 publications

References 6 publications

General massive gauge theory

General massive gauge theory

Massive vector bosons: Is the geometrical interpretation as a spontaneously broken gauge theory possible at all scales?

Beyond gauge theory: positivity and causal localization in the presence of vector mesons

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