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TMF, 1986, Volume 68, Number 3, Pages 323–337 (Mi tmf5186)  

This article is cited in 5 scientific papers (total in 5 papers)

Propagation of waves in a randomly inhomogeneous medium with strongly developed fluctuations. II. Infrared representation and large-distance behavior

L. Ts. Adzhemyan, A. N. Vasil'ev, Yu. M. Pis'mak

Leningrad State University

Abstract: In the first part of the present study [1], the problem was treated by the method that employs the renormalization group and the $4-\varepsilon$ expansion, and this was shown to be ineffective at the actual values of the parameters. In this, the second part of the study, the problem of the infrared divergences in the case of massless noise with correlation function $1/k^2$ is studied directly in three-dimensional space by means of an infrared perturbation theory of the type developed by Fradkin [2]. Summation of the infrared divergences leads to an integral representation for the propagator that, first, is completely free of infrared singularities on the mass shell and, second, exactly reproduces when expanded with respect to the coupling constant the series of ordinary perturbation theory. This representation is used to calculate the coordinate asymptotic behavior of the propagator at large distances, and it is shown that instead of the ordinary damping of the type $\exp(-\beta r)$ the damping $\exp(-\beta r\ln (r/r_0))$ is obtained, the parameter $r_0$ also being determined. Moreover, in the momentum representation the singularity of the propagator disappears altogether through the physical mass's becoming infinite on account of the infrared divergences. Such a mechanism is of interest in connection with the quark confinement problem in quantum chromodynamics.

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English version:
Theoretical and Mathematical Physics, 1986, 68:3, 855–865

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Received: 17.06.1985

Citation: L. Ts. Adzhemyan, A. N. Vasil'ev, Yu. M. Pis'mak, “Propagation of waves in a randomly inhomogeneous medium with strongly developed fluctuations. II. Infrared representation and large-distance behavior”, TMF, 68:3 (1986), 323–337; Theoret. and Math. Phys., 68:3 (1986), 855–865

Citation in format AMSBIB
\Bibitem{AdzVasPis86}
\by L.~Ts.~Adzhemyan, A.~N.~Vasil'ev, Yu.~M.~Pis'mak
\paper Propagation of waves in a~randomly inhomogeneous medium with strongly developed fluctuations. II.~Infrared representation and large-distance behavior
\jour TMF
\yr 1986
\vol 68
\issue 3
\pages 323--337
\mathnet{http://mi.mathnet.ru/tmf5186}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 68
\issue 3
\pages 855--865
\crossref{https://doi.org/10.1007/BF01019385}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1986G881200001}


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    This publication is cited in the following articles:
    1. L. Ts. Adzhemyan, A. N. Vasil'ev, Yu. M. Pis'mak, “Propagation of waves in a randomly inhomogeneous medium with strongly developed fluctuations. III. Arbitrary power-law noise correlation function”, Theoret. and Math. Phys., 74:3 (1988), 241–250  mathnet  crossref  isi
    2. L. Ts. Adzhemyan, A. N. Vasil'ev, Yu. M. Pis'mak, “Wave propagation in a randomly inhomogeneous medium with strongly developed fluctuations. IV. Light wave in a uniaxial liquid crystal”, Theoret. and Math. Phys., 78:2 (1989), 143–153  mathnet  crossref  isi
    3. M. Yu. Nalimov, “Goldstone singularities in the $4-\varepsilon$ expansion of the $\Phi^4$ theory”, Theoret. and Math. Phys., 80:2 (1989), 819–828  mathnet  crossref  isi
    4. L. Ts. Adzhemyan, A. N. Vasil'ev, M. M. Perekalin, Kh. Yu. Reittu, “Wave scattering in a randomly inhomogeneous medium with long-range noise correlation function $\sim1/r$”, Theoret. and Math. Phys., 84:2 (1990), 848–856  mathnet  crossref  isi
    5. N. V. Antonov, A. N. Vasil'ev, M. M. Stepanova, “Infrared asymptotics of the Feynman propagator in a simple non-Abellian model”, Theoret. and Math. Phys., 96:2 (1993), 989–993  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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