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 TMF, 1993, Volume 97, Number 3, Pages 431–451 (Mi tmf1751)

Heisenberg representation of second-quantized fields in stationary external fields and nonlinear dielectric media

A. A. Lobashev, V. M. Mostepanenko

State Technological Institute of St. Petersburg

Abstract: The Heisenberg formalism for the creation and annihilation operators of quantized fields in stationary external fields is developed. Fields with spin 0, 1/2, 1 are considered in external electromagnetic and scalar fields and in a field of stationary dielectric properties of a nonlinear medium. An elliptic operator that depends on the time as a parameter and whose eigenfunctions can be used to expand the field variables in the Heisenberg representation is constructed. The connection between the creation and annihilation Heisenberg operators and the operators found by diagonalizing the Hamiltonian by Bogolyubov transformations is established. Heisenberg equations of motion are obtained for external fields of arbitrary form. The phenomenological Hamiltonian that is widely used to describe parametric generation of light is derived in the framework of the quantum field theory, and the limits of applicability of the Hamiltonian are established.

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English version:
Theoretical and Mathematical Physics, 1993, 97:3, 1393–1404

Bibliographic databases:

Citation: A. A. Lobashev, V. M. Mostepanenko, “Heisenberg representation of second-quantized fields in stationary external fields and nonlinear dielectric media”, TMF, 97:3 (1993), 431–451; Theoret. and Math. Phys., 97:3 (1993), 1393–1404

Citation in format AMSBIB
\Bibitem{LobMos93} \by A.~A.~Lobashev, V.~M.~Mostepanenko \paper Heisenberg representation of second-quantized fields in stationary external fields and nonlinear dielectric media \jour TMF \yr 1993 \vol 97 \issue 3 \pages 431--451 \mathnet{http://mi.mathnet.ru/tmf1751} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1257881} \zmath{https://zbmath.org/?q=an:0828.46066} \transl \jour Theoret. and Math. Phys. \yr 1993 \vol 97 \issue 3 \pages 1393--1404 \crossref{https://doi.org/10.1007/BF01015770} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993NL72600010}