dorsal/arxiv
View SchemaPhase Space Representations and Perturbation Theory for Continuous-time Histories
| Authors | Aidan Burch |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701186 |
| URL | https://arxiv.org/abs/quant-ph/0701186 |
| DOI | 10.1063/1.2752009 |
| Journal | J.Math.Phys.48:072106,2007 |
Abstract
We consider two technical developments of the formalism of continuous-time histories. First, we provide an explicit description of histories of the simple harmonic oscillator on the classical histories phase space, comparing and contrasting the Q, P and Wigner representations; we conclude that a representation based on coherent states is the most appropriate. Second, we demonstrate a generic method for implementing a perturbative approach for interacting theories in the histories formalism, using the quartic anharmonic oscillator. We make use of the identification of the closed-time path (CTP) generating functional with the decoherence functional to develop a perturbative expansion for the latter up to second order in the coupling constant. We consider both configuration space and phase space histories.
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"abstract": "We consider two technical developments of the formalism of continuous-time\nhistories. First, we provide an explicit description of histories of the simple\nharmonic oscillator on the classical histories phase space, comparing and\ncontrasting the Q, P and Wigner representations; we conclude that a\nrepresentation based on coherent states is the most appropriate. Second, we\ndemonstrate a generic method for implementing a perturbative approach for\ninteracting theories in the histories formalism, using the quartic anharmonic\noscillator. We make use of the identification of the closed-time path (CTP)\ngenerating functional with the decoherence functional to develop a perturbative\nexpansion for the latter up to second order in the coupling constant. We\nconsider both configuration space and phase space histories.",
"arxiv_id": "quant-ph/0701186",
"authors": [
"Aidan Burch"
],
"categories": [
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],
"doi": "10.1063/1.2752009",
"journal_ref": "J.Math.Phys.48:072106,2007",
"title": "Phase Space Representations and Perturbation Theory for Continuous-time Histories",
"url": "https://arxiv.org/abs/quant-ph/0701186"
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