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 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 can be given, whose classical analog reproduces the equations of motion.

Coherent states for N-component fractional quantum Hall systems and their nonlinear sigma models

“…They can be seen as coherent excitations above the ground state |G = |Z = 0 . It can be proved that coherent states (35) are not orthogonal in general, but they have a nontrivial overlap…”

“…At a fundamental level, sigma fields φ describe the dynamics of Goldstone bosons in spontaneously broken field theories like the Standard Model of electroweak interactions. The frozen-Higgs possibility (4) has been explored in the literature [31,32,33,34,35], providing a Higgs-less mechanism to supply mass to the electro-weak gauge vector bosons W ± and Z through a coupling to a U(2)-invariant NLSMà la Stueckelberg [36]. Unfortunately, the recent "discovery" of a particle consistent with the Higgs boson, together with some apparent insoluble dichotomy "unitarity-renormalizability" [37] of the NLSM Higgs-less approach, have diminished importance to this program.…”

“…Unfortunately, the recent "discovery" of a particle consistent with the Higgs boson, together with some apparent insoluble dichotomy "unitarity-renormalizability" [37] of the NLSM Higgs-less approach, have diminished importance to this program. Perhaps non-canonical and non-perturbative quantization approaches like the one exposed in [38,39,35] can shed new light on this interesting problem.…”

Jet-Gauge Groups as Basic Symmetries of Non-Linear Sigma and Yang–mills Models and Quantization

“…It should be stressed that formal partial derivatives can eventually be transformed into actual partial derivatives as a consequence of the equations of motion (partially governed by the regularity of a corresponding Lagrangian). After this preamble of notation, we write a group law for a central extension of G 1,1 (M ) which involves a non-trivial co-cycle concerning the pair of variables (A µ , F µν ) as well as a pseudo-cocycle among the variables (φ, θ µ ) [10]: …”

“…In fact we introduce the evolution operatorÛ (t) ≡ exp( −i tĤ) ≡ eΩ (t) , which can be computed according to the Magnus Series [11]. We refer the reader to [10] for more details.…”