Open Access
Renormalization of the Abelian Higgs-Kibble Model
C. Becchi,A. Rouet,R. Stora +2 more
- Vol. 22, pp 1-53
TLDR
In this paper, the perturbative renormalization of the abelian Higgs-Kibble model is studied within the class of renormalizable gauges which are odd under charge conjugation.Abstract:
This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov Parasiuk Hepp-Zimmermann renormalization scheme is used throughout, including the renormalized action principle proved by Lowenstein and Lam. The whole study is based on the fulfillment to all orders of perturbation theory of the Slavnov identities which express the invariance of the Lagrangian under a supergauge type family of non-linear transformations involving the Faddeev-Popov ghosts. Direct combinatorial proofs are given of the gauge independence and unitarity of the physicalS operator. Their simplicity relies both on a systematic use of the Slavnov identities as well as suitable normalization conditions which allow to perform all mass renormalizations, including those pertaining to the ghosts, so that the theory can be given a setting within a fixed Fock space. Some simple gauge independent local operators are constructed.read more
Citations
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Hamiltonian form of the path integral for theories with a gauge freedom
Journal ArticleDOI
Consistent and Covariant Anomalies in Gauge and Gravitational Theories
William A. Bardeen,Bruno Zumino +1 more
TL;DR: In this article, the covariant forms for both the currents and the anomalies for general gauge theories in even-dimensional space-time were constructed and the results were then extended to determine the structure of gravitational anomalies.
Journal ArticleDOI
How instantons solve the U(1) problem
TL;DR: In this paper, it was shown that the anomalous U(1) symmetry of QCD can be attributed to a well-known anomaly in the regularization of the theory, which in field configurations called "instantons" can be seen to give rise to interactions that explicitly break the symmetry.
Journal ArticleDOI
On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories
TL;DR: In this article, the Ward-Takahashi identities for scalar electrodynamics in Fermi gauges are shown to imply a homogeneous first-order partial differential equation for the effective potential involving only the gauge parameter and the external scalar field.
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Perturbative analysis of the gradient flow in non-abelian gauge theories
Martin Lüscher,Peter Weisz +1 more
TL;DR: The gradient flow in non-abelian gauge theories is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner as mentioned in this paper.
References
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Regularization and Renormalization of Gauge Fields
Gerard 't Hooft,M.J.G. Veltman +1 more
TL;DR: In this article, a new regularization and renormalization procedure for gauge theories is presented, which is particularly well suited for the treatment of gauge theories and is transparent when anomalies such as the Bell-Jackiw-Adler anomaly may occur.
Journal ArticleDOI
Feynman Diagrams for the Yang-Mills Field
L. D. Faddeev,V.N. Popov +1 more
TL;DR: In this paper, a simple method for calculation of the contribution from arbitrary diagrams with closed loops was proposed, based on the method of Feynman functional integration, which is used in this paper.
Journal ArticleDOI
Renormalization of gauge theories
C. Becchi,A. Rouet,R. Stora +2 more
TL;DR: Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts as mentioned in this paper.