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 TMF, 1998, Volume 114, Number 2, Pages 233–249 (Mi tmf837)

Initial conditions in quasi-classical field theory

V. P. Maslov, O. Yu. Shvedov

M. V. Lomonosov Moscow State University

Abstract: We investigate the problem of divergences and renormalizations in the Hamiltonian formalism of quasi-classical field theory. This approach is known to involve divergences in the leading term of the expansion. Proposals have been made to eliminate the divergences by using nonequivalent representations of the canonical commutation relations at different moments of time. In this paper, we consider the Schrödinger equation with ultraviolet and infrared cutoffs. In order to remove the cutoffs, conditions are imposed on the initial state of the regularized theory in addition to the conditions imposed on the counterterms in the Hamiltonian. In the leading order of the quasi-classical expansion, we give the explicit form of these conditions, which is invariant under the evolution. This allows us to show that this approximation does not require the introduction of nonunitary evolution transformations

DOI: https://doi.org/10.4213/tmf837

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English version:
Theoretical and Mathematical Physics, 1998, 114:2, 184–197

Bibliographic databases:

Citation: V. P. Maslov, O. Yu. Shvedov, “Initial conditions in quasi-classical field theory”, TMF, 114:2 (1998), 233–249; Theoret. and Math. Phys., 114:2 (1998), 184–197

Citation in format AMSBIB
\Bibitem{MasShv98} \by V.~P.~Maslov, O.~Yu.~Shvedov \paper Initial conditions in quasi-classical field theory \jour TMF \yr 1998 \vol 114 \issue 2 \pages 233--249 \mathnet{http://mi.mathnet.ru/tmf837} \crossref{https://doi.org/10.4213/tmf837} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1756991} \zmath{https://zbmath.org/?q=an:1024.81031} \transl \jour Theoret. and Math. Phys. \yr 1998 \vol 114 \issue 2 \pages 184--197 \crossref{https://doi.org/10.1007/BF02557116} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000074933600002} 

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• http://mi.mathnet.ru/eng/tmf/v114/i2/p233

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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. Shvedov, OY, “Renormalization of spatially inhomogeneous nonequilibrium field dynamics”, Physics Letters B, 443:1–4 (1998), 373
2. V. P. Maslov, O. Yu. Shvedov, “On the Elimination of the Stueckelberg Divergences in the Hamiltonian Field Theory”, Proc. Steklov Inst. Math., 226 (1999), 100–120
3. Maslov V.P., Shvedov O.Y., “Large-N expansion as a semiclassical approximation to the third-quantized theory”, Physical Review D, 60:10 (1999), 105012
4. Shvedov, OY, “Time evolution in an external field: The unitarity paradox”, Annals of Physics, 287:2 (2001), 260
5. Baacke J., Boyanovsky D., de V.ega H.J., “Initial time singularities in nonequilibrium evolution of condensates and their resolution in the linearized approximation”, Physical Review D, 63:4 (2001), 045023
6. Baacke, J, “Nonequilibrium evolution in scalar O(N) models with spontaneous symmetry breaking”, Physical Review D, 65:6 (2002), 065019
7. Shvedov, OY, “Renormalization of Poincaré transformations in Hamiltonian semiclassical field theory”, Journal of Mathematical Physics, 43:4 (2002), 1809
8. Shvedov, OY, “Semiclassical symmetries”, Annals of Physics, 296:1 (2002), 51
9. Baacke, J, “Nonequilibrium evolution of Phi(4) theory in 1+1 dimensions in the two-particle point-irreducible formalism”, Physical Review D, 67:10 (2003), 105020
10. O. Yu. Shvedov, “Relativistically Covariant Quantum Field Theory of the Maslov Complex Germ”, Theoret. and Math. Phys., 144:3 (2005), 1296–1314
11. Baacke J., Kevlishvili N., “Initial time singularities and admissible initial states for a system of coupled scalar fields”, Physical Review D, 81:2 (2010), 023509
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