Longitudinal contributions to the vacuum polarization in the't Hooft–Veltman gauge

Mann, Robert B.; McKeon, Gerry; Phillips, S.B.

doi:10.1139/p84-156

Cited by 4 publications

(3 citation statements)

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“…This extends the one loop calculations of [17,18]. Whilst the authors of [17,18] were the first to observe that the longitudinal part of the photon is renormalized unlike in a linear gauge, we have carried out a slightly more general analysis by allowing for a covariant gauge parameter α and the inclusion of an additional coupling ξ in order to track the loop calculation in a similar way to the usual coupling constant a. The coupling ξ was not initially fixed to a specific value.…”

Section: Discussionmentioning

confidence: 82%

“…As the latter do not appear in linear covariant gauges in QED, the 't Hooft-Veltman gauge clearly could be used as a laboratory to study simple issues related to gauge field self-interaction. Indeed in [17,18] a one loop calculation showed that the corresponding covariant gauge fixing parameter was renormalized. Therefore, in light of these observations it is the purpose of this article to record the full three loop renormalization of QED in the 't Hooft-Veltman gauge.…”

Section: Introductionmentioning

confidence: 99%

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Three-loop {\overline{\mbox{MS}}} renormalization of QED in the 't Hooft–Veltman gauge

Gracey¹

2007

J. Phys. A: Math. Theor.

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Abstract. Quantum electrodynamics (QED) fixed in the 't Hooft-Veltman gauge is renormalized to three loops in the MS scheme. The β-functions and anomalous dimensions are computed as functions of the usual QED coupling and the additional coupling, ξ, which is introduced as part of the nonlinear gauge fixing condition. Similar to the maximal abelian gauge of quantum chromodynamics, the renormalization of the gauge parameter is singular.

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Section: Discussionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Three-loop {\overline{\mbox{MS}}} renormalization of QED in the 't Hooft–Veltman gauge

Gracey¹

2007

J. Phys. A: Math. Theor.

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“…Preregularization permits freedom in the parameterization of infinity and even (as in the above example) allows one to avoid such parameterizations entirely. In the above example the limit A + 0 is taken prior to computing the divergent integrals to ensure that n,, is transverse; indeed if A # 0, the Ward identities imply that there is a longitudinal component of It,, (26). We thus see that the 't Hooft-Veltman gauge can be used to generate an additional shift parameter that can absorb quadratically divergent photon mass terms to recover "transversality.…”

Section: Fig 8 Vacuum Polarization In Scalar Qedmentioning

confidence: 94%

Preregularization

Elias¹,

Mann²,

Chowdhury³

et al. 1985

Can. J. Phys.

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We describe and investigate the applicability of a recently proposed preregularization procedure in which arbitrary shift-of-integration-variable surface terms (in four dimensions) arising from loop-mementum ambiguities are constrained to absorb any contributions to unrenormalized Feynman amplitudes that violate Ward-Takahashi-Slavnov-Taylor (WTST) identities appropriate to the theory under consideration. Anomalies in WTST identities are shown to be the result of having insufficient arbitrariness in the loop momenta to accommodate the full set of Lagrangian symmetries. We demonstrate the utility of our procedure by analyzing the chiral anomaly in even dimensions, the supercurrent anomaly in N = 1 super Yang-Mills theory, and by calculations in quantum electrodynamics and Yang-Mills theory. We argue that the preregularization procedure should be particularly well suited to supersymmetric theories as a regularization-independent means of upholding super-WTST identities.Nous Ctudions l'applicabilitk d'une prockdure de preregularisation proposke rkcemment, dans laquelle des termes de surface (en quatre dimensions) dus a des decalages de variables d'intkgration provenant d'ambiguites boucle-impulsion sont contraints 5 absorber toutes les contributions aux amplitudes de Feynman non renormalisees qui violent les identitks Ward-TakahashiSlavnov-Taylor (WTST) approprikes a la thkorie considkree. On montre que les anomalies dans les identitks WTST sont le rksultat d'une insuffisance d'arbitraire, dans les boucles-impulsions, qui empkche d'accommoder au complet l'ensemble des symCtries du lagrangien. Nous dkmontrons 1'utilitC de notre prockdure en analysant l'anomalie chirale en nombre pair de dimensions, l'anomalie de supercourant en thkorie super-Yang-Mills N = 1, ainsi que par des calculs en EDQ et en thtorie Yang-Mills. Nous indiquons ainsi que le prockdure de prC-regularisation devrait ktre particulikrement bien adaptCe aux thCories supersymCtriques, comme support independant de la rkgularisation des identitts super-WTST.[Traduit par le journal]Can.

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Electrodynamics in the 't Hooft gauge, a covariant operator approach

2019

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Longitudinal contributions to the vacuum polarization in the't Hooft–Veltman gauge

Abstract: The Ward–Takahashi–Slavnov–Taylor (WTST) identities are examined in the 't Hooft–Veltman gauge ∂∙A + λA2 = 0. It is found that gauge invariance implies that there is a contribution to the longitudinal part of the vacuum polarization that is proportional to λ.

Cited by 4 publications

References 0 publications

Three-loop {\overline{\mbox{MS}}} renormalization of QED in the 't Hooft–Veltman gauge

Three-loop {\overline{\mbox{MS}}} renormalization of QED in the 't Hooft–Veltman gauge

Preregularization

Electrodynamics in the 't Hooft gauge, a covariant operator approach

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