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

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 nonlinear-sigma piece of the Lagrangian. In spite of the high nonlinearity 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 nonlinear systems, which departs from usual canonical quantization. On the quantum representation space of this extended symmetry group, a quantum Hamiltonian preserving the representation can be given, whose classical analog reproduces the equations of motion.