Gauge Transformation Properties of Vector and Tensor Potentials Revisited: a Group Quantization Approach

TL;DR

This paper explores a non-Higgs mechanism for generating mass in gauge theories through non-trivial gauge group representations, leading to a unified quantization approach for various gauge fields and a cohomological understanding of mass.

Contribution

It introduces a novel group quantization method that explains mass generation without Higgs, unifying massless and massive gauge theories with a cohomological perspective.

Findings

Mass parameters appear as central charges in the algebra of constraints.

The approach provides a unified quantization of different gauge theories.

A cohomological origin of mass is identified.

Abstract

The possibility of non-trivial representations of the gauge group on wavefunctionals of a gauge invariant quantum field theory leads to a generation of mass for intermediate vector and tensor bosons. The mass parameters m show up as central charges in the algebra of constraints, which then become of second-class nature. The gauge group coordinates acquire dynamics outside the null-mass shell and provide the longitudinal field degrees of freedom that massless bosons need to form massive bosons. This is a `non-Higgs' mechanism that could provide new clues for the best understanding of the symmetry breaking mechanism in unified field theories. A unified quantization of massless and massive non-Abelian Yang-Mills, linear Gravity and Abelian two-form gauge field theories are fully developed from this new approach, where a cohomological origin of mass is pointed out.