Dirac fermions in strong gravitational fields

TL;DR

This paper analyzes the behavior of Dirac fermions in strong gravitational and electromagnetic fields, deriving Hamiltonians, equations of motion, and comparing quantum and classical dynamics, with a focus on helicity and field interactions.

Contribution

It derives a Hermitian Dirac Hamiltonian in strong fields and explores the semiclassical limit, revealing the similarity of electromagnetic and gravitational interactions for spinning particles.

Findings

Quantum and classical equations of motion agree in strong fields.

Helicity dynamics are affected by strong gravitational and electromagnetic interactions.

Explicit squaring of the Dirac equation shows similar interactions for electromagnetic and gravitational fields.

Abstract

We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially isotropic metric. The quantum operator equations of motion are obtained and the semiclassical limit is analyzed. The comparison of the quantum mechanical and classical equations shows their complete agreement. The helicity dynamics in strong fields is discussed. Squaring the covariant Dirac equation explicitly shows a similarity of the interactions of electromagnetic and gravitational fields with a charged and spinning particle.