Deriving the static interaction between electric dipoles via the quantum gauge transformation

TL;DR

This paper derives the static interaction between electric dipoles by treating the gauge function's vector potential as an operator, extending the classical gauge transformation approach.

Contribution

It introduces a quantum treatment of the gauge transformation to derive dipole interactions, providing a novel perspective on the gauge function's role.

Findings

Static dipole interaction derived from quantum gauge transformation

Operator treatment modifies the electric field analysis

Provides new insights into dipole-field coupling mechanisms

Abstract

Gauge transformation leaves the electric and the magnetic fields unchanged as long as the gauge function is treated classically. In this paper we consider the gauge transformation commonly used to obtain the electric dipole interaction Hamiltonian in a system of dipoles and the electromagnetic field (Goeppert-Mayer transformation) and treat the vector potential that appear in the gauge function as an operator. While it modifies the electric field, the static interaction between the dipoles is derived.