Asymptotic expansion of Gaussian integrals of analytic functionals on infinite-dimensional spaces and quantum averages

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dc.creatorKhrennikov, Andrei
dc.date2005-12-20
dc.date.accessioned2026-07-07T06:56:40Z
dc.date.available2026-07-07T06:56:40Z
dc.descriptionWe study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of scaling of the covariation operator of a Gaussian measure and the second (Frechet) derivative of a functional. In this way we couple classical average (given by an infinite-dimensional Gaussian integral) and quantum average (given by the von Neumann trace formula). We can interpret this mathematical construction as a procedure of ``dequantization'' of quantum mechanics. We represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite-dimensional phase-space. This space can be represented as the space of classical fields, so quantum mechanics is represented as a projection of ``Prequantum Classical Statistical Field Theory''.
dc.descriptionMathematically rigorous presentation of previous results on Prequantum Classical Statistical Field Theory
dc.identifierhttps://arxiv.org/abs/quant-ph/0512166
dc.identifierhttp://arxiv.org/abs/quant-ph/0512166
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/106728
dc.subjectQuantum Physics
dc.titleAsymptotic expansion of Gaussian integrals of analytic functionals on infinite-dimensional spaces and quantum averages
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