Symplectic realization of electric charge in fields of monopole distributions

Autor(es)

Kupriyanov, Vladislav G. ^{[1, 2, 3]} ; Szabo, Richard J. ^{[4, 5, 6]}

Afiliação do(s) autor(es)

^[1] Tomsk State Univ, Tomsk 634050 - Russia

^[2] Univ Fed ABC, CMCC, BR-09210580 Santo Andre, SP - Brazil

^[3] Werner Heisenberg Inst, Max Planck Inst Phys, Fohringer Ring 6, D-80805 Munich - Germany

^[4] Heriot Watt Univ, Dept Math, Colin Maclaurin Bldg, Edinburgh EH14 4AS, Midlothian - Scotland

^[5] Maxwell Inst Math Sci, Edinburgh EH8 9AA, Midlothian - Scotland

^[6] Higgs Ctr Theoret Phys, Edinburgh EH9 3JZ, Midlothian - Scotland

• Tipo de documento: Artigo Científico
• Fonte: Physical Review D; v. 98, n. 4 AUG 7 2018.
• Citações Web of Science: 0

Resumo

We construct a symplectic realization of the twisted Poisson structure on the phase space of an electric charge in the background of an arbitrary smooth magnetic monopole density in three dimensions. We use the extended phase space variables to study the classical and quantum dynamics of charged particles in arbitrary magnetic fields by constructing a suitable Hamiltonian that reproduces the Lorentz force law for the physical degrees of freedom. In the source-free case the auxiliary variables can be eliminated via Hamiltonian reduction, while for nonzero monopole densities they are necessary for a consistent formulation and are related to the extra degrees of freedom usually required in the Hamiltonian description of dissipative systems. We obtain new perspectives on the dynamics of dyons and motion in the field of a Dirac monopole, which can be formulated without Dirac strings. We compare our associative phase space formalism with the approach based on nonassociative quantum mechanics, reproducing extended versions of the characteristic translation group three-cocycles and minimal momentum space volumes, and prove that the two approaches are formally equivalent. We also comment on the implications of our symplectic realization in the dual framework of nongeometric string theory and double field theory. (AU)

• Processo FAPESP: 16/04341-5 - Os aspectos clássicos e quânticos das teorias de campo nos espaços não-geométricos
• Beneficiário: Vladislav Kupriyanov
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional