Path integral quantization for massive vector bosons

TL;DR

This paper demonstrates that a Lorentz-invariant effective field theory of self-interacting massive vector bosons, under certain conditions, naturally leads to an SU(2) Yang-Mills theory with a mass term through canonical quantization and renormalizability constraints.

Contribution

It shows that a consistent, Lorentz-invariant effective field theory of massive vector bosons reduces to an SU(2) Yang-Mills theory with mass when quantized and constrained by renormalizability.

Findings

Self-interacting massive vector fields can be quantized canonically.

The theory's consistency implies an SU(2) Yang-Mills structure with mass.

Perturbative renormalizability constrains the form of the interaction.

Abstract

A parity-conserving and Lorentz-invariant effective field theory of self-interacting massive vector fields is considered. For the interaction terms with dimensionless coupling constants the canonical quantization is performed. It is shown that the self-consistency condition of this system with the second-class constraints in combination with the perturbative renormalizability leads to an SU(2) Yang-Mills theory with an additional mass term.