Non-compact Groups, Coherent States, Relativistic Wave Equations and the Harmonic Oscillator II: Physical and Geometrical Considerations

TL;DR

This paper explores the physical and geometric implications of a simple non-degenerate supermetric, connecting it to topological processes, gauge theories, and the representation of states in supersymmetric models.

Contribution

It introduces a new interpretation of non-degenerate supermetrics, links them to topological phenomena, and discusses their relation to supergravity gauge theories and state representations.

Findings

States are observables and can be seen as projections or representations of the metaplectic group.

Non-degenerate super-manifolds offer advantages over degenerate ones in geometric formulations.

The model suggests a mechanism for field localization and relates to 5D warped models.

Abstract

The physical meaning of the particularly simple non-degenerate supermetric, introduced in the previous part by the authors, is elucidated and the possible connection with processes of topological origin in high energy physics is analyzed and discussed. New possible mechanism of the localization of the fields in a particular sector of the supermanifold is proposed and the similarity and differences with a 5-dimensional warped model are shown. The relation with gauge theories of supergravity based in the $OSP(1/4)$ group is explicitly given and the possible original action is presented. We also show that in this non-degenerate super-model the physic states, in contrast with the basic states, are observables and can be interpreted as tomographic projections or generalized representations of operators belonging to the metaplectic group $Mp(2)$. The advantage of geometrical formulations based on non-degenerate super-manifolds over degenerate ones is pointed out and the description and the analysis of some interesting aspects of the simplest Riemannian superspaces are presented from the point of view of the possible vacuum solutions.