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

Journal Article · Sun Dec 01 04:00:00 EST 1996 · Physical Review A

DOI:https://doi.org/10.1103/PhysRevA.54.4691· OSTI ID:397535

Krause, J ^[1]

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1. 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, Journal Name: Physical Review A Journal Issue: 6 Vol. 54; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CASIMIR OPERATORS
GROUP THEORY
KINEMATICS
LIE GROUPS
MAGNETIC FIELD EFFECTS
MAGNETIC FIELDS
POINT CHARGE
QUANTIZATION
QUANTUM MECHANICS
QUANTUM OPERATORS
SCHROEDINGER EQUATION