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Journal ArticleDOI

Renormalization of gauge theories

01 Jun 1976-Annals of Physics (Academic Press)-Vol. 98, Iss: 2, pp 287-321
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.
About: This article is published in Annals of Physics.The article was published on 1976-06-01 and is currently open access. It has received 1551 citations till now. The article focuses on the topics: BRST quantization & Introduction to gauge theory.

Summary (1 min read)

1 -Introduction

  • The analysis can thus be successfully carried out when this lie algebra 1s semisimple -1f the obstruction provided by the Adleir Bardeen [10] anomaly is absent.
  • The authors shall thus carry out sost of their analysis in the «:er«-simple £ase, and only wa*e a few remarks concerning some of the phenomena *hicb occur when abelian components are involved.

75/P.723 Conclusion

  • Gauge theories can be characterized by the fulfillment of Slavnov identities when the underlying Lie algebra is semi-simple, i.e. is suffi ciently rigid against perturbations.
  • Then, simple power counting arguments are sufficient to prove that, indeed Slavnov identities can be fulfilled, in the absence of Adler Bardeen anomalies.
  • It is believed that both the lack of rigidity of the underlying Lie algebra and the possible occurrence of Adler Bardeen anomalies can only be mastered by more sophisticated tools based on a closer analysis of the consistency conditions involving the behaviour of the theory under di latations [7] , [20] .
  • The analysis of gauge independent local operators, although not touched upon here [l] should also be tractable in terms of the methods used here.

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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.

928 citations

Journal ArticleDOI

751 citations

01 Jan 1975
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.

747 citations

Journal ArticleDOI
TL;DR: In this paper, recent progress made towards the understanding of closed bosonic and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean space-time, is devoted to recent progress.
Abstract: This paper is devoted to recent progress made towards the understanding of closed bosonic and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean space-time. Special emphasis is put on the fundamental role of Riemann surfaces and supersurfaces. The differential and complex geometry of their moduli space is developed as needed. New results for the superstring presented here include the supergeometric construction of amplitudes, their chiral and superholomorphic splitting and a global formulation of supermoduli space and amplitudes.

721 citations

Journal ArticleDOI
TL;DR: In this paper, the general nonlinear scalar model is studied at asymptotically low temperature near two dimensions, and the low temperature expansion is renormalized and effective algorithms are derived for calculation to all orders in the renormalised expansion.

691 citations

References
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Book
01 Jan 1971
TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.
Abstract: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements. Ce premier volume du Livre sur les Groupes et algebre de Lie, neuvieme Livre du traite, est consacre aux concepts fondamentaux pour les algebres de Lie. Il comprend les paragraphes: - 1 Definition des algebres de Lie; 2 Algebre enveloppante d une algebre de Lie; 3 Representations; 4 Algebres de Lie nilpotentes; 5 Algebres de Lie resolubles; 6 Algebres de Lie semi-simples; 7 Le theoreme d Ado. Ce volume est une reimpression de l edition de 1971."

3,256 citations

Journal ArticleDOI
TL;DR: In this article, the axial-vector vertex in spinor electrodynamics has anomalous properties which differ with those found by the formal manipulation of field equations, and the divergence of axial vector current is not the usual expression calculated from the field equations.
Abstract: Working within the framework of perturbation theory, we show that the axial-vector vertex in spinor electrodynamics has anomalous properties which disagree with those found by the formal manipulation of field equations. Specifically, because of the presence of closed-loop "triangle diagrams," the divergence of axial-vector current is not the usual expression calculated from the field equations, and the axial-vector current does not satisfy the usual Ward identity. One consequence is that, even after the external-line wave-function renormalizations are made, the axial-vector vertex is still divergent in fourth- (and higher-) order perturbation theory. A corollary is that the radiative corrections to ${\ensuremath{ u}}_{l}l$ elastic scattering in the local current-current theory diverge in fourth (and higher) order. A second consequence is that, in massless electrodynamics, despite the fact that the theory is invariant under ${\ensuremath{\gamma}}_{5}$ tranformations, the axial-vector current is not conserved. In an Appendix we demonstrate the uniqueness of the triangle diagrams, and discuss a possible connection between our results and the ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ decays. In particular, we argue that as a result of triangle diagrams, the equations expressing partial conservation of axial-vector current (PCAC) for the neutral members of the axial-vector-current octet must be modified in a well-defined manner, which completely alters the PCAC predictions for the ${\ensuremath{\pi}}^{0}$ and the $\ensuremath{\eta}$ two-photon decays.

3,232 citations

Journal ArticleDOI
TL;DR: In this paper, the anomalous Ward identities are shown to satisfy consistency or integrability relations, which restrict their possible form, for the case of SU(3) × SU(1) and for SU(2) + SU (3) + 2.

2,450 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: 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.

1,045 citations

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Q1. What have the authors contributed in "Renormalization of gauge theories" ?

In this paper, the authors present conditions générales d'utilisation ( http: //www.numdam.org/conditions ).