Coherent and semiclassical states in a magnetic field in the presence of the Aharonov-Bohm solenoid

A new approach to constructing coherent states (CS) and semiclassical states (SS) in a magnetic-solenoid field is proposed. The main idea is based on the fact that the AB solenoid breaks the translational symmetry in the xy-plane; this has a topological effect such that there appear two types of trajectories which embrace and do not embrace the solenoid. Due to this fact, one has to construct two different kinds of CS/SS which correspond to such trajectories in the semiclassical limit. Following this idea, we construct CS in two steps, first the instantaneous CS (ICS) and then the time-dependent CS/SS as an evolution of the ICS. The construction is realized for nonrelativistic and relativistic spinning particles both in (2 + 1) and (3 + 1) dimensions and gives a non-trivial example of SS/CS for systems with a nonquadratic Hamiltonian. It is stressed that CS depending on their parameters (quantum numbers) describe both pure quantum and semiclassical states. An analysis is represented that classifies parameters of the CS in such respect. Such a classification is used for the semiclassical decompositions of various physical quantities.

Russian Science and Innovations Federal Agency

Russian Science and Innovations Federal Agency[02.740.11.0238]

Russia President grant[SS-3400.2010.2]

Russia President grant

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

FAPESP/Brasil

CAPES/Brasil

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

FAPESP

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

CNPq

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)