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Generating Functionals for Harmonic Expectation Values of Paths with Fixed End Points. Feynman Diagrams for Nonpolynomial Interactions

Hagen Kleinert·Axel Pelster·Michael Bachmann
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Abstract

We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating functionals are calculated explicitly for harmonic oscillators with time-dependent frequency, and used to derive a smearing formulas for correlation functions of polynomial and nonpolynomials functions of time-dependent positions and momenta. These formulas summarize the effect of thermal and quantum fluctuations, and serve to derive generalized Wick rules and Feynman diagrams for perturbation expansions of nonpolynomial interactions.

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Hagen Kleinert, Axel Pelster, Michael Bachmann. 1999-02-15. Generating Functionals for Harmonic Expectation Values of Paths with Fixed End Points. Feynman Diagrams for Nonpolynomial Interactions. https://doi.org/10.1103/physreve.60.2510

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