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Symplectic geometry on an infinite-dimensional phase space and an asymptotic representation of quantum averages by Gaussian functional integrals
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. matematik. (matematik)ORCID iD: 0000-0002-9857-0938
2008 (English)In: Izvestiya. Mathematics, ISSN 1064-5632, E-ISSN 1468-4810, Vol. 72, no 1, p. 127-148Article in journal (Refereed) Published
Abstract [en]

We study the relation between the mathematical structures of statistical mechanics on an infinite-dimensional phase space (denoted by ) and quantum mechanics. It is shown that quantum averages (given by the von Neumann trace formula) can be obtained as the main term of the asymptotic expansion of Gaussian functional integrals with respect to a small parameter . Here is the dispersion of the Gaussian measure. The symplectic structure on the infinite-dimensional phase space plays a crucial role in our considerations. In particular, the Gaussian measures that induce quantum averages must be consistent with the symplectic structure. The equations of Schrödinger, Heisenberg and von Neumann are images of the Hamiltonian dynamics on .

Place, publisher, year, edition, pages
2008. Vol. 72, no 1, p. 127-148
Keywords [en]
Symplectic geometry, infinite-dimensional phase space, asymptotic representation, quantum averages, Gaussian integrals
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:vxu:diva-3873DOI: 10.1070/IM2008v072n01ABEH002395OAI: oai:DiVA.org:vxu-3873DiVA, id: diva2:203830
Available from: 2009-01-03 Created: 2009-01-03 Last updated: 2017-12-13Bibliographically approved

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Publisher's full texthttp://databas.bib.vxu.se:2451/summary.do?product=WOS&qid=1&SID=V2DFjiKBJjbef8afooO&search_mode=GeneralSearch&formValue(summary_mode)=GeneralSearch&page=2

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Khrennikov, Andrei

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More styles
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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  • asciidoc
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