O(3,1) symmetry problem of the charge--monopole interaction

Journal Article · Thu Jan 01 04:00:00 EST 1987 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527802· OSTI ID:6698080

Feher, L G

The question of whether there exists a smooth, time-independent conserved vector observable in the classical mechanics of the charge--monopole interaction that spans an O(3,1) Lie algebra together with the angular momentum or not is examined. It turns out that any candidate for such dynamical symmetry algebra has hard singularities at that part of the phase space that corresponds to charge--monopole collisions. In the course of the investigation we use the transformation of Boulware et al. (D. G. Boulware, L. S. Brown, R. N. Cahn, S. D. Ellis, and C. Lee, Phys. Rev. D 14, 2708 (1976)) relating the charge--monopole system to a point mass moving in an inverse square potential. This transformation is shown to be a complete isomorphism between the scattering parts of the related Hamiltonian systems; its global behavior is described in terms of an U(1) principal fiber bundle of nontrivial topology. Several remarks on the symmetries of various monopole problems are made, e.g., the most general O(4) symmetry algebra is given for a special form of the charge--dyon interaction.

• Research Organization: Bolyai Institute, H-6720 Szeged, Hungary
• OSTI ID: 6698080
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 28:1; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645202* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Electromagnetic Interactions & Properties
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
ANGULAR MOMENTUM
BASIC INTERACTIONS
CLASSICAL MECHANICS
ELECTROMAGNETIC INTERACTIONS
ELEMENTARY PARTICLES
HAMILTONIANS
INTERACTIONS
LIE GROUPS
MAGNETIC MONOPOLES
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
MONOPOLES
PARTICLE INTERACTIONS
POSTULATED PARTICLES
POTENTIALS
QUANTUM OPERATORS
SYMMETRY
SYMMETRY GROUPS