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Wiener Integration for Quantum Systems: A Unified Approach to the Feynman-Kac Formula

  • Bernhard Bodmann
  • Simone Warzel
Part of the NATO ASI Series book series (NSSB, volume 361)

Abstract

Gaussian linearization on the basis of Wiener integration over operator-valued functionals provides a unifying approach to the probabilistic representation of certain operator semigroups [B. Bodmann, H. Leschke, S. Warzel, in: Path integrals: Dubna’ 96, eds. V. S. Yarunin, M. A. Smondyrev, Dubna 1996, pp. 95–106]. Within the setting of a quantum particle in an electromagnetic field it naturally yields a basis independent version of the standard Feynman-Kac(-Ito) formula for the corresponding Schrödinger semigroup. In this framework even semigroups generated by non-standard Hamiltonians such as for a quantum particle with a spatially dependent mass can be represented by conventional Wiener integrals — in contrast to [B. Gaveau, L. S. Schulman: J. Math. Phys. 30, (1989) 2019]. The approach offers a convenient starting point for estimations and calculations.

Keywords

Unify Approach Path Integral Ward Identity Functional Integration Quantum Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Bernhard Bodmann
    • 1
  • Simone Warzel
    • 1
  1. 1.Institut für Theoretische PhysikUniversität Erlangen-NürnbergErlangenGermany

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