Off-center coherent-state representation and an application to semiclassics

TL;DR

This paper introduces a novel off-center coherent-state representation using overcomplete sets, leading to a new quantum representation and a generalized semiclassical propagator, which could improve long-standing semiclassical propagation methods.

Contribution

It presents an alternative unit operator form based on off-center coherent states and derives a generalized semiclassical propagator for localized states.

Findings

Derived a new off-center coherent-state representation.

Established a family of non-unique reproducing kernels.

Proposed a generalized semiclassical propagator extending van Vleck's formula.

Abstract

By using the overcompleteness of coherent states we find an alternative form of the unit operator for which the ket and the bra appearing under the integration sign do not refer to the same phase-space point. This defines a new quantum representation in terms of Bargmann functions, whose basic features are presented. A continuous family of secondary reproducing kernels for the Bargmann functions is obtained, showing that this quantity is not necessarily unique for representations based on overcomplete sets. We illustrate the applicability of the presented results by deriving a semiclassical expression for the Feynman propagator that generalizes the well-known van Vleck formula and seems to point a way to cope with long-standing problems in semiclassical propagation of localized states.