The Zeeman Effect for the Relativistic Bound State

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 µ and restricting the support of the eigenfunctions in spacetime to the subspace of the Minkowski measure space, for which (x ⊥) 2 = [x − (x · n)n] 2 ≥ 0. In this paper, we examine the Zeeman effect for these bound states, which requires n µ to be a dynamical quantity. We recover the usual Zeeman splitting in a manifestly covariant form.