The Zeeman Effect for the Relativistic Bound State

Abstract

In the context of a relativistic quantum mechanics with invariant evolution parameter, solutions for the relativistic bound state problem have been found, which yield a spectrum for the total mass coinciding with the nonrelativistic Schrödinger energy spectrum. These spectra were obtained by choosing an arbitrary spacelike unit vector $n_{\mu }$ and restricting the support of the eigenfunctions in spacetime to the subspace of the Minkowski measure space, for which $(x_{\perp }{)}^2=[x-(x\cdot n)n{]}^2\ge 0$. In this paper, we examine the Zeeman effect for these bound states, which requires $n_{\mu }$ to be a dynamical quantity. We recover the usual Zeeman splitting in a manifestly covariant form.

21 pages, TAUP-2150-94

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