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Renormalization of the Abelian Higgs-Kibble Model

01 Jan 1975-Vol. 22, pp 1-53
TL;DR: 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.

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Citations
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Journal ArticleDOI
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.

1,551 citations

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Book
30 May 2011
TL;DR: In this article, a systematic treatment of perturbative QCD is given, giving an accurate account of the concepts, theorems and their justification, giving strong motivations for the methods.
Abstract: The most non-trivial of the established microscopic theories of physics is QCD: the theory of the strong interaction. A critical link between theory and experiment is provided by the methods of perturbative QCD, notably the well-known factorization theorems. Giving an accurate account of the concepts, theorems and their justification, this book is a systematic treatment of perturbative QCD. As well as giving a mathematical treatment, the book relates the concepts to experimental data, giving strong motivations for the methods. It also examines in detail transverse-momentum-dependent parton densities, an increasingly important subject not normally treated in other books. Ideal for graduate students starting their work in high-energy physics, it will also interest experienced researchers wanting a clear account of the subject.

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References
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Journal ArticleDOI
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.

3,722 citations

Book
01 Jan 2006

2,553 citations

Journal ArticleDOI

2,530 citations

Journal ArticleDOI
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.

1,646 citations

Journal ArticleDOI
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.

1,551 citations