The space-time torsion in the context of the Exact Foldy-Wouthuysen Transformation for a Dirac fermion

TL;DR

This paper introduces a new involution operator enabling an exact Foldy-Wouthuysen transformation for Dirac fermions in space-time torsion fields, resolving previous inconsistencies and discussing potential experimental implications.

Contribution

A novel involution operator is proposed to perform exact transformations of Dirac fields interacting with torsion, improving upon semi-exact methods.

Findings

Resolved inconsistency in Foldy-Wouthuysen transformation with torsion

Presented bound state solutions for the theory

Discussed potential experimental tests

Abstract

In this work we focus our attention in the inconsistency that appears when the Semi-Exact Foldy-Wouthuysen transformation for the Dirac field interacting with space-time torsion field is performed. In order to solve this problem, we present a new involution operator that makes possible to perform the exact transformation when torsion field is present. Such operator has a structure, well known in the literature, composed of the product of an operator that acts in the matrices space and another one that acts in the function space. We also present the bound state of this theory and discuss the possible experimental analysis.