Abstract
We examine the problem of incorporating external electromagnetic interactions into the theory of the relativistic infinite-component SO(4,2) wave equation for the hydrogen atom proposed by Barut. We introduce the simplest set of covariant interaction terms modeled after the nonrelativistic SO(4,2) theory as an alternative to the complicated array of terms obtained from the formal replacement ${P}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{P}_{\ensuremath{\mu}}\ensuremath{-}e{A}_{\ensuremath{\mu}}$. Using a covariant perturbation theory, we calculate the electric and magnetic polarizabilities of the ground state of the hydrogen atom in uniform fields and show that they have the correct nonrelativistic reductions.
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