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Feynman path integrals and Lebesgue–Feynman measures

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Abstract

The definition of Feynman path integrals (Feynman functional integrals) as integrals with respect to a generalized measure, called the Lebesgue–Feynman measure in the paper and being an infinite-dimensional analogue of the classical Lebesgue measure on finite-dimensional Euclidean space, is discussed. This definition, which is a formalization of Feynman’s original definition, is different from those used previously in the mathematical literature. It makes it possible to give a description of the origin of quantum anomaly which is a mathematically correct version of the description given in the book Path Integrals and Quantum Anomalies by K. Fujikawa and H. Suzuki (Oxford, 2004) (and erroneously qualified as wrong in the book Functional Integration: Action and Symmetries by P. Cartier and C. DeWitt-Morette (Cambridge Univ. Press, Cambridge, 2006)).

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Author information

Authors and Affiliations

  1. School of Mathematics, University of Manchester, Manchester, M13 9PL, UK

    J. Montaldi

  2. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    O. G. Smolyanov

Authors
  1. J. Montaldi
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  2. O. G. Smolyanov
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Corresponding author

Correspondence to O. G. Smolyanov.

Additional information

Original Russian Text © J. Montaldi, O.G. Smolyanov, 2017, published in Doklady Akademii Nauk, 2017, Vol. 475, No. 5, pp. 490–495.

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Montaldi, J., Smolyanov, O.G. Feynman path integrals and Lebesgue–Feynman measures. Dokl. Math. 96, 368–372 (2017). https://doi.org/10.1134/S1064562417040226

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  • DOI: https://doi.org/10.1134/S1064562417040226

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