Coherent state path integral for linear systems

C. G. Torre
Phys. Rev. D 72, 025004 – Published 12 July 2005

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.

  • Received 30 March 2005

DOI:https://doi.org/10.1103/PhysRevD.72.025004

©2005 American Physical Society

Authors & Affiliations

C. G. Torre

  • Department of Physics, Utah State University, Logan, Utah 84322-4415, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 72, Iss. 2 — 15 July 2005

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×