On the Coherent State Path Integral for Linear Systems

Details On the Coherent State Path Integral for Linear Systems On the Coherent State Path Integral for Linear Systems

2005-03-28

arxiv.org/abs/quant-ph/0503213v1

Phys.Rev. D72 (2005) 025004

Physics

Quantum Physics

15 pages, plain TeX

Scientific paper

10.1103/PhysRevD.72.025004

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.

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