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.




This research has been supported by the National Science Foundation (Grant No. PHY-1710856) and by the Missouri Research Board.

Keywords and Phrases

Gauge invariance; Gauge transformation; General expression; Polarizabilities; Radiative and relativistic corrections; Radiative corrections; Scalar and vector potentials; Transition currents, Wave functions

International Standard Serial Number (ISSN)

2469-9926; 2469-9934

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2018 American Physical Society (APS), All rights reserved.

Publication Date

01 Jun 2018

Included in

Physics Commons