Lorentz Gauge Theory and Spinor Interaction

TL;DR

This paper formulates a Lorentz gauge theory emphasizing spinor and vector differences, explores torsion in curved space-time, and generalizes the Pauli equation for spinor interactions with a new gauge field.

Contribution

It introduces a gauge theory of the Lorentz group based on spinor-vector behavior differences and analyzes spinor interactions with a new gauge field in both flat and curved space-time.

Findings

Formulation of a Lorentz gauge theory in flat space-time.

Analysis of torsion's role in curved space-time.

Generalization of the Pauli equation for spinor interactions.

Abstract

A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.