Abstract:
A formal scheme is proposed for considering the quantum theory of a single-component scalar
field φ(x)φ(x) with essentially nonlinear Lagrangian interaction of the form
LI(x)=g∞∑n=0unn!:φn(x):,LI(x)=g∞∑n=0unn!:φn(x):,
where unun is a sequence of numbers which satisfy certain general equations. Reasons are given in favor of the fact that within the bounds of the proposed scheme, a form factor can be selected such that the SS-matrix constructed for Lagrangian interaction LI(x)LI(x) should be finite and unitary in every order of perturbation theory.
Citation:
G. V. Efimov, “Essentially nonlinear interaction Lagrangians and nonlocalized quantum field theory”, TMF, 2:1 (1970), 36–54; Theoret. and Math. Phys., 2:1 (1970), 26–40
\Bibitem{Efi70}
\by G.~V.~Efimov
\paper Essentially nonlinear interaction Lagrangians and nonlocalized quantum field theory
\jour TMF
\yr 1970
\vol 2
\issue 1
\pages 36--54
\mathnet{http://mi.mathnet.ru/tmf3987}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=471758}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 2
\issue 1
\pages 26--40
\crossref{https://doi.org/10.1007/BF01028853}
Linking options:
https://www.mathnet.ru/eng/tmf3987
https://www.mathnet.ru/eng/tmf/v2/i1/p36
This publication is cited in the following 3 articles:
Guskov V.A. Ivanov M.G. Ogarkov S.L., “A Note on Efimov Nonlocal and Nonpolynomial Quantum Scalar Field Theory”, Phys. Part. Nuclei, 52:3 (2021), 420–437
Ivan Chebotarev, Vladislav Guskov, Stanislav Ogarkov, Matthew Bernard, “S-Matrix of Nonlocal Scalar Quantum Field Theory in Basis Functions Representation”, Particles, 2:1 (2019), 103
Sergio Albeverio, Raphael Høegh-Krohn, “Uniqueness of the physical vacuum and the Wightman functions in the infinite volume limit for some non polynomial interactions”, Commun.Math. Phys., 30:3 (1973), 171
Citation in format AMSBIB
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