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

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

2009-06-19

arxiv.org/abs/0906.3638v1

Found.Phys.39:373-396,2009

Physics

High Energy Physics

High Energy Physics - Theory

Stile of the text improved in Journal

Scientific paper

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.

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