Quantum kinematic theory of a point charge in a constant magnetic field

A group-theoretic quantization method is applied to the ‘‘complete symmetry group’’ describing the motion of a point charge in a constant magnetic field. Within the regular ray representation, the Schrödinger operator is obtained as the Casimir operator of the extended Lie algebra. Configuration ray representations of the complete group cast the Schrödinger operator into the familiar space-time differential operator. Next, ‘‘group quantization’’ yields the superselection rules, which produce irreducible configuration ray representations. In this way, the Schrödinger operator becomes diagonalized, together with the angular momentum. Finally, the evaluation of an invariant integral, over the group manifold, gives rise to the Feynman propagation kernel 〈t′,x′|t,x〉 of the system. Everything stems from the assumed symmetry group. Neither canonical quantization nor the path-integral method is used in the present analysis. © 1996 The American Physical Society.