Coherent states, vacuum structure and infinite component relativistic wave equations

TL;DR

This paper analyzes the structure of solutions to Dirac-type wave equations with internal variables, revealing their relation to coherent states and showing that their symmetries correspond to the Metaplectic group rather than the Lorentz group.

Contribution

It provides the general solution to the problem of wave equations with internal variables, clarifies the physical spectrum, and identifies the relevant symmetry group as the Metaplectic group Mp(n).

Findings

Physical states are represented by coherent states.

Previous solutions are not the most general.

Symmetries correspond to the Metaplectic group, not Lorentz.

Abstract

It is commonly claimed in the recent literature that certain solutions to wave equations of positive energy of Dirac-type with internal variables are characterized by a non-thermal spectrum. As part of that statement, it was said that the transformations and symmetries involved in equations of such type correspond to a particular representation of the Lorentz group. In this paper we give the general solution to this problem emphasizing the interplay between the group structure, the corresponding algebra and the physical spectrum. This analysis is completed with a strong discussion and proving that: i) the physical states are represented by coherent states; ii) the solutions in previous references [1] are not general, ii) the symmetries of the considered physical system in [1] (equations and geometry) do not correspond to the Lorentz group but to the fourth covering: the Metaplectic group Mp(n).