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 non-relativistic Schrodinger energy spectrum. These spectra were obtained by choosing an arbitrary spacelike unit vector n, and restricting the support of the eigenfunctions in spacetime to the subspace of the Minkowski measure space, for which (X_{perpendicular to})²=(x-(x.n)n)²>or=0. In this paper, we examine the normal Zeeman effect (in lowest order) for these bound states, which requires n_mu to be a dynamical quantity. We recover the usual Zeeman splitting in a manifestly covariant form.