Phase space representations and perturbation theory for continuous-time histories
Jan, 200723 pages
Published in:
- J.Math.Phys. 48 (2007) 072106
e-Print:
- quant-ph/0701186 [quant-ph]
DOI:
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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.Note:
- 22 pages; slightly shortened, more concise argumentation; ref. added
- 03.65.Ge
- 03.65.Ta
- 03.65.Ca
- perturbation theory
- harmonic oscillators
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