Quantum kinematic theory of a point charge in a constant magnetic field
- Facultad de Fisica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile)
A group-theoretic quantization method is applied to the {open_quote}{open_quote}complete symmetry group{close_quote}{close_quote} describing the motion of a point charge in a constant magnetic field. Within the regular ray representation, the Schr{umlt o}dinger operator is obtained as the Casimir operator of the extended Lie algebra. Configuration ray representations of the complete group cast the Schr{umlt o}dinger operator into the familiar space-time differential operator. Next, {open_quote}{open_quote}group quantization{close_quote}{close_quote} yields the superselection rules, which produce irreducible configuration ray representations. In this way, the Schr{umlt o}dinger 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 {l_angle}{ital t}{prime},{bold x}{prime}{vert_bar}{ital t},{bold x}{r_angle} of the system. Everything stems from the assumed symmetry group. Neither canonical quantization nor the path-integral method is used in the present analysis. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 397535
- Journal Information:
- Physical Review A, Vol. 54, Issue 6; Other Information: PBD: Dec 1996
- Country of Publication:
- United States
- Language:
- English
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