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Dirac particle in a magnetic field: Symmetries and their breaking by monopole singularities

Journal Article · · Phys. Rev., D; (United States)

Some rules governing motion of a charged particle obeying the Dirac equation are assembled, including exact helicity conservation for scattering on an arbitrary finite magnetic field configuration. The singularity at the location of a magnetic monopole invalidates the derivation of the rules mentioned, leaving the Dirac Hamiltonian H undefined for the lowest angular momentum state of the electron in the field of the pole. Specifying the behavior of H under the discrete P, T, and C symmetries determines it almost uniquely. One result is that H may possess a bound state of zero energy, contrary to assertions in early papers on the subject. Zero-energy bound states which violate the superselection rule for electric charge are also studied, including one which is the point limit of a solution for a fermion multiplet interacting with a finite-energy soliton monopole. Implications of such a bound state for second quantization have been considered previously by others and are further analyzed here. The suggestion that monopoles may possess half-integral fermion number is shown to be unwarranted by present evidence.

Research Organization:
Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794
OSTI ID:
5441383
Journal Information:
Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 16:6; ISSN PRVDA
Country of Publication:
United States
Language:
English

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Related Subjects

645202* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Electromagnetic Interactions & Properties
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANGULAR MOMENTUM
BOUND STATE
BOUNDARY CONDITIONS
CHARGED PARTICLES
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELEMENTARY PARTICLES
EQUATIONS
HAMILTONIANS
HELICITY
LIE GROUPS
MAGNETIC MONOPOLES
MATHEMATICAL OPERATORS
MONOPOLES
PARTICLE PROPERTIES
POSTULATED PARTICLES
QUANTUM OPERATORS
SCATTERING AMPLITUDES
SELECTION RULES
SU GROUPS
SU-2 GROUPS
SUPERSELECTION RULES
SYMMETRY BREAKING
SYMMETRY GROUPS
WAVE EQUATIONS