Algebraic characterization of constraints and generation of mass in gauge theories

TL;DR

This paper explores how non-trivial gauge group representations in gauge-invariant quantum field theories can generate mass for vector and tensor bosons through algebraic modifications of constraints.

Contribution

It introduces an algebraic framework where mass parameters emerge as central charges, transforming constraints and providing longitudinal degrees of freedom for massive bosons.

Findings

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

Constraints become second-class due to non-trivial gauge group representations.

Gauge group coordinates gain dynamics, enabling massive boson formation.

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.