Coherent states for a 2-sphere with a magnetic field

TL;DR

This paper constructs and analyzes coherent states for a particle on a 2-sphere under a magnetic field, extending previous nonmagnetic models using the complexifier approach and heat kernel methods.

Contribution

It introduces a new class of coherent states for a magnetic 2-sphere system using the complexifier method, expanding the framework beyond Perelomov states.

Findings

Coherent states are labeled by phase space points on the sphere.

They are eigenvectors of specific annihilation operators.

A Segal--Bargmann representation with resolution of identity is established.

Abstract

We consider a particle moving on a 2-sphere in the presence of a constant magnetic field. Building on earlier work in the nonmagnetic case, we construct coherent states for this system. The coherent states are labeled by points in the associated phase space, the (co)tangent bundle of S^2. They are constructed as eigenvectors for certain annihilation operators and expressed in terms of a certain heat kernel. These coherent states are not of Perelomov type, but rather are constructed according to the "complexifier" approach of T. Thiemann. We describe the Segal--Bargmann representation associated to the coherent states, which is equivalent to a resolution of the identity.