Anti-BRST in the Causal Approach

TL;DR

This paper investigates whether anti-BRST symmetry can provide additional constraints to eliminate anomalies in Yang-Mills theories within the causal approach, concluding it does not offer new restrictions beyond BRST invariance.

Contribution

The study shows that anti-BRST invariance does not impose new restrictions beyond BRST invariance in the causal approach to Yang-Mills theories.

Findings

Anti-BRST invariance up to second order matches BRST invariance.

Anti-BRST transform offers no new constraints for anomaly elimination.

Likely, the result holds in all orders of perturbation theory.

Abstract

It is known that the elimination of the anomalies in all orders of perturbation theory is an open problem. The constrains given by usual invariance properties and the Wess-Zumino identities are not enough to eliminate the anomalies in the general case of an 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 the perturbation theory, we also have anti-BRST invariance up to the same order. Probably, this result is true in all orders of the 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.