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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

A white noise approach to phase space Feynman path integrals


Authors: W. Bock and M. Grothaus
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 85 (2011).
Journal: Theor. Probability and Math. Statist. 85 (2012), 7-22
MSC (2010): Primary 60H40, 46F25
Published electronically: January 11, 2013
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Abstract: The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schrödinger equation are obtained and the canonical commutation relations are satisfied. The latter can be shown, since we not only construct the integral but rather the Feynman integrand and the corresponding generating functional.


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Additional Information

W. Bock
Affiliation: Functional Analysis and Stochastic Analysis Group, Department of Mathematics, University of Kaiserslautern, 67653 Kaiserslautern, Germany
Email: bock@mathematik.uni-kl.de

M. Grothaus
Affiliation: Functional Analysis and Stochastic Analysis Group, Department of Mathematics, University of Kaiserslautern, 67653 Kaiserslautern, Germany
Email: grothaus@mathematik.uni-kl.de

DOI: http://dx.doi.org/10.1090/S0094-9000-2013-00870-9
PII: S 0094-9000(2013)00870-9
Keywords: White noise analysis, Feynman integrals, mathematical physics
Received by editor(s): December 3, 2010
Published electronically: January 11, 2013
Additional Notes: The authors would like to thank the organizing and programme committee of the MSTAII conference for an interesting an stimulating meeting. Wolfgang Bock wants especially thank to Yuri Kondratiev for the opportunity to give a talk on this topic at the conference. Furthermore, the authors would like to thank Florian Conrad, Anna Hoffmann, Tobias Kuna and Ludwig Streit for helpful discussions. The financial support from the DFG project GR 1809/9-1, which enabled the authors to join the conference, is thankfully acknowledged
The paper is based on the talk presented at the International Conference “Modern Stochastics: Theory and Applications II” held on September 7–11, 2010 at Kyiv National Taras Shevchenko University and dedicated to three anniversaries of prominent Ukrainian scientists: Anatolii Skorokhod, Volodymyr Korolyuk and Igor Kovalenko.
Dedicated: We dedicate this article to Anatolii Skorohod, Volodymyr Korolyuk and Igor Kovalenko
Article copyright: © Copyright 2013 American Mathematical Society