Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes

TL;DR

This paper develops a covariant relativistic quantum framework for Proca particles in curved spacetimes, incorporating electromagnetic interactions and transformations that unify quantum and classical descriptions.

Contribution

It formulates covariant equations for Proca particles with electromagnetic moments in Riemannian spacetimes and performs a Foldy-Wouthuysen transformation consistent with classical limits.

Findings

Hamiltonian matches classical and Dirac particle Hamiltonians

Covariant equations include anomalous magnetic and electric dipole moments

Unification of relativistic quantum mechanics in Foldy-Wouthuysen representation

Abstract

Relativistic quantum mechanics of a Proca (spin-1) particle in Riemannian spacetimes is constructed. Covariant equations defining electromagnetic interactions of a Proca particle with the anomalous magnetic moment and the electric dipole moment in Riemannian spacetimes are formulated. The relativistic Foldy-Wouthuysen transformation with allowance for terms proportional to the zero power of the Planck constant is performed. The Hamiltonian obtained agrees with the corresponding Foldy-Wouthuysen Hamiltonians derived for scalar and Dirac particles and with their classical counterpart. The unification of relativistic quantum mechanics in the Foldy-Wouthuysen representation is discussed.