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Mat. Sb., 1989, Volume 180, Number 6, Pages 763–786 (Mi msb1633)  

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


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.

Full text: PDF file (1313 kB)
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English version:
Mathematics of the USSR-Sbornik, 1990, 67:1, 209–233

Bibliographic databases:

UDC: 517.444
MSC: Primary 81E05, 58G15; Secondary 81D07
Received: 07.07.1987 and 20.12.1988

Citation: A. Yu. Khrennikov, “The correspondence principle in quantum field theory and relativistic boson string theory”, Mat. Sb., 180:6 (1989), 763–786; 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 Mat. Sb.
\yr 1989
\vol 180
\issue 6
\pages 763--786
\mathnet{http://mi.mathnet.ru/msb1633}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=834173}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 67
\issue 1
\pages 209--233
\crossref{https://doi.org/10.1070/SM1990v067n01ABEH001362}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1990ED88000013}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Yu. Khrennikov, “Quantum mechanics over non-Archimedean number fields”, Theoret. and Math. Phys., 83:3 (1990), 623–632  mathnet  crossref  mathscinet  zmath  isi
    3. Khrennikov A., “Pseudodifferential-Operators on Non-Archimedean Spaces”, Differ. Equ., 26:6 (1990), 767–776  mathnet  mathscinet  zmath  isi
    4. Khrennikov A., “Representation of the Secondary Quantization Over Non-Archimedean Numerical Fields”, 314, no. 6, 1990, 1380–1384  mathscinet  zmath  isi
    5. Khrennikov A., “Schrodinger and Bargman-Fock Representations in Non-Archimedean Quantum-Mechanics”, 313, no. 2, 1990, 325–329  mathscinet  zmath  isi
    6. A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. Yu. Khrennikov, “Generalized functions and Gaussian path integrals over non-archimedean function spaces”, Math. USSR-Izv., 39:1 (1992), 761–794  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. A. Yu. Khrennikov, “The infinite-dimensional Liouville equation”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 17–41  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. Khrennikov A., “Feynman-Katz Formula on Phase Superspace .1.”, Differ. Equ., 28:8 (1992), 1180–1189  mathnet  mathscinet  zmath  isi
    10. A. Yu. Khrennikov, R. Cianci, “Nonlinear evolution equations with (1,1)-supersymmetric time”, Theoret. and Math. Phys., 97:2 (1993), 1267–1272  mathnet  crossref  mathscinet  zmath  isi
    11. Roberto Cianci, Andrew Khrennikov, “Differential equations with supersymmetric time”, Lett Math Phys, 30:4 (1994), 279  crossref  mathscinet  zmath  isi  elib
    12. Khrennikov A., “A Pre-Quantum Classical Statistical Model with Infinite-Dimensional Phase Space”, J. Phys. A-Math. Gen., 38:41 (2005), 9051–9073  crossref  mathscinet  zmath  adsnasa  isi
    13. Khrennikov A., “On the Problem of Hidden Variables for Quantum Field Theory”, Nouvo Cimento Soc. Ital. Fis. B-Gen. Phys. Relativ. Astron. Math. Phys. Methods, 121:5 (2006), 505–521  crossref  mathscinet  isi
    14. Khrennikov A., “Fourier Analysis Over Hyperbolic Algebra, Pseudo-Differential Operators, and Hyperbolic Deformation of Classical Mechanics”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 10:3 (2007), 421–438  crossref  mathscinet  zmath  isi
    15. A. Yu. Khrennikov, “Symplectic geometry on an infinite-dimensional phase space and an asymptotic representation of quantum averages by Gaussian functional integrals”, Izv. Math., 72:1 (2008), 127–148  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. Khrennikov A., “Hyperbolic Quantization”, Adv. Appl. Clifford Algebr., 18:3-4, SI (2008), 843–852  crossref  mathscinet  zmath  isi
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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