Fermion Dynamics by Internal and Space-Time Symmetries

TL;DR

This paper develops a gauge theory of the Lorentz group incorporating internal and space-time symmetries, analyzing fermion behavior, torsion effects, and stationary solutions in both flat and curved space-time.

Contribution

It introduces a novel gauge theory of the Lorentz group based on ambiguities in isometric diffeomorphisms, extending fermion dynamics analysis to include new gauge fields and torsion effects.

Findings

Fermion fields transform under local Lorentz transformations.

Torsion field influences fermion dynamics in curved space-time.

Stationary solutions reveal spinor structure in hydrogen-like atoms.

Abstract

This manuscript is devoted to introduce a gauge theory of the Lorentz Group based on the ambiguity emerging in dealing with isometric diffeo-morphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be ordinary world vectors) are analyzed in flat space-time and the role of the torsion field, within the generalization to curved space-time, is briefly discussed. The fermion dynamics is then analyzed including the new gauge fields and assuming time-gauge. Stationary solutions of the problem are also analyzed in the non-relativistic limit, to study the spinor structure of an hydrogen-like atom.