https://doi.org/10.1140/epjp/s13360-025-06820-0
Regular Article
The Feynman-Kac formula in deformation quantization
1
Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Campus Pedregal, Av. Parque Chapultepec 1610, Col. Privadas del Pedregal, 78217, San Luis Potosí, SLP, Mexico
2
Dipartimento di Fisica “Ettore Pancini”, Universitá degli studi di Napoli “Federico II”, Complesso Univ. Monte S. Angelo, I-80126, Napoli, Italy
3
Departamento de Física, Centro de Investigación y de Estuios Avanzados del IPN, P.0. Box 14-740, 07000, Ciudad de México, Mexico
a
jasel.berra@uaslp.mx
b
alberto.molgado@uaslp.mx
Received:
23
April
2025
Accepted:
2
September
2025
Published online:
13
September
2025
We introduce the Feynman-Kac formula within the deformation quantization program. Inferred from the previous work, it is shown that, upon a Wick rotation, the ground state energy of any prescribed physical system can be obtained from the asymptotic limit of the phase space integration of the star exponential of the Hamiltonian function. Some examples of this correspondence are provided showing a novel and efficient way of computing the ground state energy for some physical models.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
