Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field

TL;DR

This paper derives a Hamiltonian for relativistic scalar particles, including massless ones, in an electromagnetic field using generalized transformations, revealing quantum effects like quadrupole coupling and polarizabilities.

Contribution

It introduces a generalized transformation approach that applies to massless particles and shows the Hamiltonian's form is independent of arbitrary parameters.

Findings

Hamiltonian includes quantum quadrupole and polarizability terms.

Derived equations of motion for massive and massless particles.

Applicable to massless particles in electromagnetic fields.

Abstract

We successively apply the generalized Case-Foldy-Feshbach-Villars (CFFV) and the Foldy-Wouthuysen (FW) transformation to derive the Hamiltonian for relativistic scalar particles in an electromagnetic field. In contrast to the original transformation, the generalized CFFV transformation contains an arbitrary parameter and can be performed for massless particles, which allows solving the problem of massless particles in an electromagnetic field. We show that the form of the Hamiltonian in the FW representation is independent of the arbitrarily chosen parameter. Compared with the classical Hamiltonian for point particles, this Hamiltonian contains quantum terms characterizing the quadrupole coupling of moving particles to the electric field and the electric and mixed polarizabilities. We obtain the quantum mechanical and semiclassical equations of motion of massive and massless particles in an electromagnetic field.