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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On the gauge fixed BRST cohomology
Marc Henneaux,Marc Henneaux +1 more
TL;DR: In this article, it was shown that the antifields in question are not the usual invariants associated with the gauge invariant description, but instead are adapted to the gauge fixation.
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An algebraic proof on the finiteness of Yang-Mills-Chern-Simons theory in D=3
TL;DR: In this article, a rigorous algebraic proof of finiteness in all orders of perturbation theory is given for the Yang-Mills-Chern-Simons theory in a general three-dimensional Riemannian manifold.
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On the equivalence of the background field method
Anton Rebhan,G. Wirthumer +1 more
TL;DR: In this paper, an improved and generalized version of a recent proof of equivalence for S-matrices obtained in the background field method and in conventional quantization procedures is proposed, and it is shown explicitly that theS-matrix is independent of the additional arbitrary gauge breaking term.
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Slavnov-Taylor parameterization of Yang-Mills theory with massive fermions in the presence of singlet axial-vector currents
TL;DR: In this article, the Slavnov-Taylor identities for Yang-Mills theory with massive fermions in the presence of singlet axial vector currents were restored and a natural set of normalization conditions were derived allowing to reduce the algebraic complexity of higher orders up to a homogeneous linear problem.
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Higher nilpotent analogues of A∞-structure
TL;DR: In this paper, Shakirov et al. proposed a higher nilpotent analogization of the A ∞ -structure on simplicial complexes, which they called (D n ) n = ( ∑ i = 1 ∞ m n (i ) ) ) ○ n = 0, which is defined on triangulated manifolds (tetrahedral lattices) and deformation D n = U n d n U n −1 is defined with the help of the n-versions of exterior product ⋀ n.
References
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Journal ArticleDOI
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.
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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.