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

TL;DR

This paper introduces a novel method for constructing coherent and semiclassical states in magnetic fields with Aharonov-Bohm solenoids, accounting for topological effects and different trajectory types.

Contribution

It presents a new approach to build coherent and semiclassical states considering the topological influence of the AB solenoid, applicable to both nonrelativistic and relativistic particles in various dimensions.

Findings

Constructed two types of CS/SS for trajectories embracing or not embracing the solenoid.

Provided a classification of CS parameters for quantum and semiclassical states.

Applied the method to systems with nonquadratic Hamiltonians.

Abstract

A new approach to constructing coherent states (CS) and semiclassical states (SS) in 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 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.