Manifestly covariant canonical quantization II: Gauge theory and anomalies

TL;DR

This paper extends a covariant canonical quantization method to gauge theories, revealing a new type of anomaly linked to the observer's trajectory that affects unitarity and is usually overlooked in traditional field theory.

Contribution

It introduces a covariant quantization approach for gauge theories that uncovers a novel anomaly related to the observer's trajectory, differing from conventional anomalies.

Findings

Gauge algebra acquires an abelian extension proportional to the quadratic Casimir.

The anomaly is compatible with unitarity and is not detectable in standard field theory.

A well-defined charge operator exists despite the anomaly.

Abstract

In hep-th/0411028 a new manifestly covariant canonical quantization method was developed. The idea is to quantize in the phase space of arbitrary histories first, and impose dynamics as first-class constraints afterwards. The Hamiltonian is defined covariantly as the generator of rigid translations of the fields relative to the observer. This formalism is now applied to theories with gauge symmetries, in particular electromagnetism and Yang-Mills theory. The gauge algebra acquires an abelian extension proportional to the quadratic Casimir operator. Unlike conventional gauge anomalies proportional to the third Casimir, this is not inconsistent. On the contrary, a well-defined and non-zero charge operator is only compatible with unitarity in the presence of such anomalies. This anomaly is invisible in field theory because it is a functional of the observer's trajectory, which is conventionally ignored.