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arXiv · hep-th/9407075

The Zeeman Effect for the Relativistic Bound State

M. C. Land·L. P. Horwitz
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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 $n_μ$ and restricting the support of the eigenfunctions in spacetime to the subspace of the Minkowski measure space, for which $(x_\perp )^2 = [x-(x \cdot n) n ]^2 \geq 0$. 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.

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M. C. Land, L. P. Horwitz. 1994-07-14. The Zeeman Effect for the Relativistic Bound State. https://doi.org/10.1088/0305-4470%2F28%2F11%2F025

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