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TMF, 1971, Volume 9, Number 3, Pages 355–364 (Mi tmf4500)  

This article is cited in 2 scientific papers (total in 2 papers)

Regularization of the equations of the quantum theory for a scalar neutral field with selfinteraction in the case of two spatial degrees of freedom

L. G. Zastavenko


Abstract: The method developed earlier [1] is applied to the more complicated case of two spatial coordinates. The equations for the ground and excited states are of the same form as in the one-dimensional case, but the integrations are substituted by double ones. The divergencies more complicated than those in the one-dimensional case arise. However they can be avoided by means of extracting a certain special factor from the eigen-functional $\Omega$ of the energy operator $H$.

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English version:
Theoretical and Mathematical Physics, 1971, 9:3, 1191–1198

Received: 23.03.1969
Revised: 25.06.1971

Citation: L. G. Zastavenko, “Regularization of the equations of the quantum theory for a scalar neutral field with selfinteraction in the case of two spatial degrees of freedom”, TMF, 9:3 (1971), 355–364; Theoret. and Math. Phys., 9:3 (1971), 1191–1198

Citation in format AMSBIB
\Bibitem{Zas71}
\by L.~G.~Zastavenko
\paper Regularization of the equations of the quantum theory for a~scalar neutral field with selfinteraction in the case of two spatial degrees of freedom
\jour TMF
\yr 1971
\vol 9
\issue 3
\pages 355--364
\mathnet{http://mi.mathnet.ru/tmf4500}
\transl
\jour Theoret. and Math. Phys.
\yr 1971
\vol 9
\issue 3
\pages 1191--1198
\crossref{https://doi.org/10.1007/BF01043409}


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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. L. G. Zastavenko, “Partial allowance for the self-interaction in a very simplf model of quantum field theory”, Theoret. and Math. Phys., 10:1 (1972), 38–41  mathnet  crossref
    2. L. G. Zastavenko, “Reduction of the problem of calculating the class of infinite-multiplicity integrals in quantum field theory to the solution of an integral equation”, Theoret. and Math. Phys., 20:1 (1974), 660–666  mathnet  crossref  zmath
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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