The covariant Stark effect

M. C. Land*, L. P. Horwitz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrödinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the nonrelativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is linear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter.

Original languageEnglish
Pages (from-to)967-991
Number of pages25
JournalFoundations of Physics
Issue number6
StatePublished - Jun 2001


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