Abstract
A constant homogeneous magnetic field is applied to a composite system madeup of two scalar particles with opposite charges. Motion is described by a pairof coupled Klein=nGordon equations that are written in closed form with help ofa suitable representation. The relativistic symmetry associated with the magneticfield is carefully respected. Considering eigenstates of the pseudomomentumfour-vector, we separate out collective variables and obtain a three-dimensionalreduced equation, posing a nonconventional eigenvalue problem. The velocityof the system as a whole (with respect to the frames where the field is purelymagnetic) generates “motional terms” in the formulas; these terms are taken intoaccount within a manifestly covariant framework.
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Droz-Vincent, P. Two-Body Mass-Shell Constraints in a Constant Magnetic Field (Neutral Case). International Journal of Theoretical Physics 39, 389–403 (2000). https://doi.org/10.1023/A:1003696528314
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DOI: https://doi.org/10.1023/A:1003696528314