Relativistic and Radiative Corrections to the Dynamic Stark Shift: Gauge Invariance and Transition Currents in the Velocity Gauge

TL;DR

This paper examines the gauge invariance of the dynamic Stark shift, revealing the necessity of additional transition current corrections in the velocity gauge, especially for radiative and relativistic effects.

Contribution

It introduces a general expression for transition current corrections needed for gauge invariance in the velocity gauge during dynamic Stark shift calculations.

Findings

Gauge invariance holds only with transition current corrections.

Derived a general formula for transition current in the velocity gauge.

Applied formalism to radiative and relativistic Stark shift corrections.

Abstract

We investigate the gauge invariance of the dynamic (ac) Stark shift under "hybrid" gauge transformations from the "length" (E.r) to the "velocity" (A.p) gauge. By a "hybrid" gauge transformation, we understand a transformation in which the scalar and vector potentials are modified, but the wave function remains unaltered. The gauge invariance of the leading term is well known, while we here show that gauge invariance under perturbations holds only if one takes into account an additional correction to the transition current, which persists only in the velocity gauge. We find a general expression for this current, and apply the formalism to radiative and relativistic corrections to the dynamic Stark effect, which is described by the sum of two polarizability matrix elements.