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Generating functionals for harmonic expectation values of paths with fixed end points: Feynman diagrams for nonpolynomial interactions

1999/02/15 by H. Kleinert, Hagen Kleinert, Axel Pelster +1 · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Feynman diagram #Harmonic oscillator #Mathematical analysis #Mathematical physics #Mathematics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Polynomial #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #quant-ph

paper · pdf · doi:10.1103/physreve.60.2510

published as Phys.Rev. E60 (1999) 2510 · Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/281

arxiv created 1999/02/15 · openalex publication_date 1999/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 the harmonic oscillator with time-dependent frequency, and used to derive a smearing formula for correlation functions of polynomial and nonpolynomial functions of time-dependent positions and momenta. This formula summarizes the effect of quantum fluctuations, and serves to derive generalized Wick rules and Feynman diagrams for perturbation expansions of nonpolynomial interactions.

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