dorsal/arxiv
View SchemaAsymptotic expansion of Gaussian integrals of analytic functionals on infinite-dimensional spaces and quantum averages
| Authors | Andrei Khrennikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512166 |
| URL | https://arxiv.org/abs/quant-ph/0512166 |
Abstract
We 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''.
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"abstract": "We study asymptotic expansions of Gaussian integrals of analytic functionals\non infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an\nasymptotic equality coupling the Gaussian integral and the trace of the\ncomposition of scaling of the covariation operator of a Gaussian measure and\nthe second (Frechet) derivative of a functional. In this way we couple\nclassical average (given by an infinite-dimensional Gaussian integral) and\nquantum average (given by the von Neumann trace formula). We can interpret this\nmathematical construction as a procedure of ``dequantization\u0027\u0027 of quantum\nmechanics. We represent quantum mechanics as an asymptotic projection of\nclassical statistical mechanics with infinite-dimensional phase-space. This\nspace can be represented as the space of classical fields, so quantum mechanics\nis represented as a projection of ``Prequantum Classical Statistical Field\nTheory\u0027\u0027.",
"arxiv_id": "quant-ph/0512166",
"authors": [
"Andrei Khrennikov"
],
"categories": [
"quant-ph"
],
"title": "Asymptotic expansion of Gaussian integrals of analytic functionals on infinite-dimensional spaces and quantum averages",
"url": "https://arxiv.org/abs/quant-ph/0512166"
},
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