Comptes Rendus
Mathematical Physics
Generalized infinite-dimensional Fresnel integrals
Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 255-259.

A generalized infinite dimensional oscillatory integral with a polynomially growing phase function is defined and explicitly computed in terms of an absolutely convergent Gaussian integral. The results are applied to the Feynman path integral representation for the solution of the Schrödinger equation with an anharmonic oscillator potential.

Un concept d'intégrale oscillatoire généralisée en dimension infinie, avec une fonction de phase de croissance, polynomiale à l'infini, est introduit. L'intégrale est calculée explicitement en termes d'intégrales gaussiennes absolument convergentes. Les résultats sont appliqués à une representation de type « intégrale sur les chemins de Feynman » de la solution de l'équation de Schrödinger à potentiel anharmonique.

Published online:
DOI: 10.1016/j.crma.2003.11.022

Sergio Albeverio 1, 2; Sonia Mazzucchi 2

1 Institut für Angewandte Mathematik, Wegelerstr. 6, 53115 Bonn, Germany
2 Dipartimento di Matematica, Università di Trento, 38050 Povo, Italy
     author = {Sergio Albeverio and Sonia Mazzucchi},
     title = {Generalized infinite-dimensional {Fresnel} integrals},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {255--259},
     publisher = {Elsevier},
     volume = {338},
     number = {3},
     year = {2004},
     doi = {10.1016/j.crma.2003.11.022},
     language = {en},
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Sergio Albeverio; Sonia Mazzucchi. Generalized infinite-dimensional Fresnel integrals. Comptes Rendus. Mathématique, Volume 338 (2004) no. 3, pp. 255-259. doi : 10.1016/j.crma.2003.11.022.

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