Symmetry group of massive Yang-Mills theories without Higgs and their quantization

TL;DR

This paper explores the symmetry structure of massive Yang-Mills theories without Higgs, proposing a novel quantization method based on an extended symmetry group that handles the non-linear scalar sector.

Contribution

It introduces a group-theoretical quantization approach for non-linear massive Yang-Mills theories with an extended symmetry group, bypassing traditional canonical methods.

Findings

Identifies an infinite symmetry extension of the gauge group in these models.

Develops a quantization algorithm tailored for non-linear systems.

Constructs a quantum Hamiltonian consistent with the extended symmetries.

Abstract

We analyze the symmetry group of massive Yang-Mills theories and their quantization strongly motivated by an already proposed alternative to the Standard Model of electroweak interactions without Higgs. In these models the mass generation of the intermediate vector bosons is based on a non-Abelian Stueckelberg mechanism where the dynamics of the Goldstone-like bosons is addressed by a partial-trace Non-Linear-Sigma piece of the Lagrangian. In spite of the high non-linearity of the scalar sector, the existence of an infinite number of symmetries, extending the traditional gauge group, allows us to sketch a group-theoretical quantization algorithm specially suited to non-linear systems, which departs from usual canonical quantization. On the quantum representation space of this extended symmetry group, a quantum Hamiltonian preserving the representation is given, whose classical analog reproduces the equations of motion.