Phase Space Representations and Perturbation Theory for Continuous-time Histories

Details Phase Space Representations and Perturbation Theory for Continuous-time Histories Phase Space Representations and Perturbation Theory for Continuous-time Histories

2007-01-25

arxiv.org/abs/quant-ph/0701186v2

J.Math.Phys.48:072106,2007

Physics

Quantum Physics

22 pages; slightly shortened, more concise argumentation; ref. added

Scientific paper

10.1063/1.2752009

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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