dorsal/arxiv
View SchemaOn the Coherent State Path Integral for Linear Systems
| Authors | C. G. Torre |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503213 |
| URL | https://arxiv.org/abs/quant-ph/0503213 |
| DOI | 10.1103/PhysRevD.72.025004 |
| Journal | Phys.Rev. D72 (2005) 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.
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"abstract": "We present a computation of the coherent state path integral for a generic\nlinear system using ``functional methods\u0027\u0027 (as opposed to discrete time\napproaches). The Gaussian phase space path integral is formally given by a\ndeterminant built from a first-order differential operator with coherent state\nboundary conditions. We show how this determinant can be expressed in terms of\nthe symplectic transformation generated by the (in general, time-dependent)\nquadratic Hamiltonian for the system. We briefly discuss the conditions under\nwhich the coherent state path integral for a linear system actually exists. A\nnecessary -- but not sufficient -- condition for existence of the path integral\nis that the symplectic transformation generated by the Hamiltonian is\n(unitarily) implementable on the Fock space for the system.",
"arxiv_id": "quant-ph/0503213",
"authors": [
"C. G. Torre"
],
"categories": [
"quant-ph",
"gr-qc",
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"math.MP"
],
"doi": "10.1103/PhysRevD.72.025004",
"journal_ref": "Phys.Rev. D72 (2005) 025004",
"title": "On the Coherent State Path Integral for Linear Systems",
"url": "https://arxiv.org/abs/quant-ph/0503213"
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