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.
U. D. Jentschura and C. M. Adhikari, "Relativistic and Radiative Corrections to the Dynamic Stark Shift: Gauge Invariance and Transition Currents in the Velocity Gauge," Physical Review A, vol. 97, no. 6, American Physical Society (APS), Jun 2018.
The definitive version is available at https://doi.org/10.1103/PhysRevA.97.062120
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)
Article - Journal
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