Functional versus canonical quantization of a nonlocal massive vector-gauge theory

TL;DR

This paper compares functional and canonical quantization methods for a nonlocal massive gauge theory derived from topological mass generation, ensuring consistency between approaches and analyzing the spectrum and nonlocality issues.

Contribution

It demonstrates the equivalence of path integral and canonical quantization for a nonlocal gauge theory and addresses the challenges of nonlocality and infinite degrees of freedom.

Findings

Propagators match between path integral and canonical formalisms.

Canonical formalism can handle nonlocal theories with infinite derivatives.

Nonlocality manifests in the spectrum and commutator structure.

Abstract

It has been shown in literature that a possible mechanism of mass generation for gauge fields is through a topological coupling of vector and tensor fields. After integrating over the tensor degrees of freedom, one arrives at an effective massive theory that, although gauge invariant, is nonlocal. Here we quantize this nonlocal resulting theory both by path integral and canonical procedures. This system can be considered as equivalent to one with an infinite number of time derivatives and consequently an infinite number of momenta. This means that the use of the canonical formalism deserves some care. We show the consistency of the formalism we use in the canonical procedure by showing that the obtained propagators are the same as those of the (Lagrangian) path integral approach. The problem of nonlocality appears in the obtainment of the spectrum of the theory. This fact becomes very transparent when we list the infinite number of commutators involving the fields and their velocities.