A Novel Approach to Lorentz Gauge Theory

TL;DR

This paper introduces a new gauge theory for the Lorentz group, analyzing how fermion fields and spin connections behave under local transformations, and discusses the role of torsion in curved spacetime.

Contribution

It presents a novel gauge theory framework for the Lorentz group, focusing on isometric diffeomorphisms and the behavior of fermions and spin connections in curved spacetime.

Findings

Analysis of local Lorentz transformations on fermion fields

Discussion of torsion's role in curved spacetime

Framework for Lorentz gauge theory based on isometric diffeomorphisms

Abstract

This paper is devoted to introduce a gauge theory of the Lorentz Group based on the analysis of isometric diffeomorphism-induced Lorentz transformations. The behaviors under local transformations of fermion fields and spin connections (assumed to be coordinate vectors) are analyzed and the role of the torsion field in a curved space-time is discussed.