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Mathematics of the USSR-Sbornik, 1990, Volume 67, Issue 1, Pages 209–233
DOI: https://doi.org/10.1070/SM1990v067n01ABEH001362
(Mi sm1633)
 

This article is cited in 16 scientific papers (total in 16 papers)

The correspondence principle in quantum field theory and relativistic boson string theory

A. Yu. Khrennikov
References:
Abstract: The author constructs the Schrödinger representation in the quantum theory of fields, strings, and membranes on a mathematical level of rigor. This representation is based on the theory of pseudodifferential operators on an infinite-dimensional superspace, developed by the author within the framework of functional superanalysis.
In the Schrödinger representation, the author realizes all the basic operators of quantum mechanics with fermion-boson coordinates, the operators of quantum field theory (including supersymmetric field theory), and the operators of the quantum and field theory of strings and membranes (Hamiltonians of fields with polynomial self-action in a space of arbitrary dimension. Virasoro operators, the BRST charge operator which forms the basis of boson string gauge theory, the gauge-invariant Hamiltonian of a boson string, and the Hamiltonian of a supermembrane).
It should be noted that the representation constructed here does not satisfy the canonical axiomatics of quantum theory ? the state space is not Hilbert space.
Bibliography: 45 titles.
Received: 07.07.1987 and 20.12.1988
Bibliographic databases:
UDC: 517.444
MSC: Primary 81E05, 58G15; Secondary 81D07
Language: English
Original paper language: Russian
Citation: A. Yu. Khrennikov, “The correspondence principle in quantum field theory and relativistic boson string theory”, Math. USSR-Sb., 67:1 (1990), 209–233
Citation in format AMSBIB
\Bibitem{Khr89}
\by A.~Yu.~Khrennikov
\paper The correspondence principle in quantum field theory and relativistic boson string theory
\jour Math. USSR-Sb.
\yr 1990
\vol 67
\issue 1
\pages 209--233
\mathnet{http://mi.mathnet.ru//eng/sm1633}
\crossref{https://doi.org/10.1070/SM1990v067n01ABEH001362}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=834173}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1990ED88000013}
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  • https://doi.org/10.1070/SM1990v067n01ABEH001362
  • https://www.mathnet.ru/eng/sm/v180/i6/p763
  • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1989–1990 Sbornik: Mathematics
     
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