Perturbative Gauge Anomalies in the Hamiltonian Formalism: A Cohomological Analysis

TL;DR

This paper uses cohomological methods within the Hamiltonian formalism to analyze gauge anomalies, showing their equivalence to Lagrangian anomalies and confirming Faddeev's conjecture relating gauge anomalies to Schwinger terms.

Contribution

It provides a gauge and regularisation independent proof linking gauge anomalies in Hamiltonian systems to those in Lagrangian formalism, confirming Faddeev's conjecture.

Findings

Anomalies appear in the time development of the BRST charge.

Anomalies violate the nilpotency of the BRST charge.

Gauge anomalies are equivalent in Hamiltonian and Lagrangian formalisms.

Abstract

The quantum action principle of renormalisation theory is applied to the antibracket-antifield formalism for Hamiltonian systems. General results on the local BRST cohomology allow one to prove that the anomalies appear in the time development of the BRST charge and violate the nilpotency of this charge. Furthermore they are equivalent to those of the Lagrangian formalism. The analysis provides a completely gauge and regularisation independent proof of Faddeev's conjecture on the relationship between gauge anomalies and Schwinger terms in the context of descent equations.