All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Physical Review D

Volume

72

Issue

2

Publisher

American Physical Society

Publication Date

2005

First Page

025004-1

Last Page

025004-7

DOI

10.1103/PhysRevD.72.025004

Abstract

We present a computation of the coherent state path integral for a generic linear system using "functional methods'' (as opposed to discrete time approaches). The Gaussian phase space path integral is formally given by a determinant built from a first-order differential operator with coherent state boundary conditions. We show how this determinant can be expressed in terms of the symplectic transformation generated by the (in general, time-dependent) quadratic Hamiltonian for the system. We briefly discuss the conditions under which the coherent state path integral for a linear system actually exists. A necessary -- but not sufficient -- condition for existence of the path integral is that the symplectic transformation generated by the Hamiltonian is (unitarily) implementable on the Fock space for the system.

Comments

Originally published by the American Physical Society. Publisher's PDF available through Physical Review D - Particles, Fields, Gravitation, and Cosmology.

http://arxiv.org/abs/quant-ph/0503213