Abstract
It is known that the elimination of anomalies in all orders of perturbation theory is an open problem. The constraints given by usual invariance properties and the Wess–Zumino identities are not enough to eliminate the anomalies in the general case of a Yang–Mills theory. So, any new symmetry of the model could restrict further the anomalies and be a solution of the problem. We consider the anti-BRST transform of Ojima in the causal approach and investigate if such new restrictions are obtained. Unfortunately, the result is negative: if we have BRST invariance up to the second order of perturbation theory, we also have anti-BRST invariance up to the same order. Probably, this result is true in all orders of perturbation theory. So, anti-BRST transform gives nothing new, and we have to find other ideas to restrict and eventually eliminate the anomalies for a general Yang–Mills theory.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
In this paper we will use the causal approach to perturbative quantum field theory: this the Epstein–Glaser prescription adapted to gauge models by G
If we describe them by fields carrying only physical degrees of freedom, the theories are usually not renormalizable
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The general framework of perturbation theory consists of the construction of some distribution-valued operators called chronological products [1]. In this paper we will use the causal approach to perturbative quantum field theory: this the Epstein–Glaser prescription adapted to gauge models by G. We say that the theory is gauge invariant in all orders of perturbation theory if the following set of identities generalizing (6): n dQ T I1 ,...,In = i ∑ (−1)sl l =1. Such identities can be usually broken by anomalies, i.e., expressions of the type.
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