On the Coherent State Path Integral for Linear Systems

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.

arXiv comment15 pages, plain TeX

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• Functional Evolution of Free Quantum Fields
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• On Unitary Time Evolution in Gowdy $T^3$ Cosmologies
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Cited by in corpus (2)

• Functional integrals and inequivalent representations in Quantum Field Theory
• Generalized generating functional for mixed-representation Green's functions: A quantum mechanical approach