Propagator for a spin 1/2 particle in terms of the unitary representations of the Lorentz group

TL;DR

This paper develops a relativistic quantum framework for spin-1/2 particles using unitary Lorentz group representations, providing a new way to compute transition amplitudes in a generalized Heisenberg picture.

Contribution

It introduces a novel approach to describe relativistic fermions via Lorentz group representations, extending previous non-relativistic results.

Findings

Constructs transition amplitudes using two-component functions

Provides a Lorentz-invariant description of fermion dynamics

Extends previous non-relativistic models to relativistic case

Abstract

In this paper we extend our previous result on the description of the partcle motion in a generalized Heisenberg picture to a relativistic fermion. The operators of the Lorentz algebra in this picture may be regarded as field operators. In this approach the transition amplitudes for the particle are constructed in terms of two-component functions in the unitary representations of the Lorentz group.