An analysis on the convergence of equal-time commutators and the closure of the BRST algebra in Yang-Mills theories

Abstract

In renormalizable theories, we define equal-time commutators (ETC'S) in terms of the equal-time limit and investigate its convergence in perturbation theory. We find that the equal-time limit vanishes for amplitudes with the effective dimension $d_{\em eff} \leq -2$ and is finite for those with $d_{\em eff} =-1$ but without nontrivial discontinuity. Otherwise we expect divergent equal-time limits. We also find that, if the ETC's involved in verifying an Jacobi identity exist, the identity is satisfied. Under these circumstances, we show in the Yang-Mills theory that the ETC of the $0$ component of the BRST current with each other vanishes to all orders in perturbation theory if the theory is free from the chiral anomaly, from which we conclude that $[Q,Q]=0$, where $Q$ is the BRST charge. For the case that the chiral anomaly is not canceled, we use various broken Ward identities to show that $[Q,Q]$ is finite and $[Q,[Q,Q]]$ vanishes at the one-loop level and that they start to diverge at the two-loop level unless there is some unexpected cancellation mechanism that improves the degree of convergence.

35 pages

References in corpus (3)

• On the finiteness of the BRS modulo-d cocycles
• A new insight into BRST anomalies in string theory
• Unrecognizable Black Holes in Two Dimensions

Cited by in corpus (4)

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• The Gauss Law Operator Algebra and Double Commutators in Chiral Gauge Theories
• Schwinger terms in 1+1 dimensions
• BFV-BRST Quantization of 2D Supergravity