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TMF, 1975, Volume 25, Number 2, Pages 147–163 (Mi tmf4060)  

This article is cited in 30 scientific papers (total in 32 papers)

Quantization of solitons

V. E. Korepin, L. D. Faddeev

Abstract: The quantization of particle-like solutions is considered on the example of the Sine–Gordon equation. Quasi-classical approximation is shown to be good when the coupling constant is small. Quantum corrections are calculated with the aid of the functional integral.

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English version:
Theoretical and Mathematical Physics, 1975, 25:2, 1039–1049

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Received: 02.04.1975

Citation: V. E. Korepin, L. D. Faddeev, “Quantization of solitons”, TMF, 25:2 (1975), 147–163; Theoret. and Math. Phys., 25:2 (1975), 1039–1049

Citation in format AMSBIB
\by V.~E.~Korepin, L.~D.~Faddeev
\paper Quantization of solitons
\jour TMF
\yr 1975
\vol 25
\issue 2
\pages 147--163
\jour Theoret. and Math. Phys.
\yr 1975
\vol 25
\issue 2
\pages 1039--1049

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. Ya. Aref'eva, “Conservation laws for the four-fermion interaction in two-dimensional spacetime”, Theoret. and Math. Phys., 26:3 (1976), 205–207  mathnet  crossref  mathscinet
    2. I. V. Volovich, “Quasicalssical expansion in quantum field theory and solitons”, Theoret. and Math. Phys., 29:1 (1976), 901–905  mathnet  crossref  mathscinet
    3. P. P. Kulish, E. R. Nisimov, “Anomalies of quantum currents in exactly solvable models”, Theoret. and Math. Phys., 29:2 (1976), 992–998  mathnet  crossref  mathscinet  zmath  isi
    4. V. A. Andreev, “Application of the inverse scattering method to the equation $\sigma_{xt}=e^\sigma$”, Theoret. and Math. Phys., 29:2 (1976), 1027–1032  mathnet  crossref  mathscinet
    5. A. V. Razumov, O. A. Khrustalev, “Application of Bogolyubov's method to quantization of boson fields in the neighborhood of a classical solution”, Theoret. and Math. Phys., 29:3 (1976), 1084–1090  mathnet  crossref  mathscinet
    6. A. V. Razumov, “Bogolyubov transformation and quantization of solitons”, Theoret. and Math. Phys., 30:1 (1977), 10–16  mathnet  crossref  mathscinet
    7. A. N. Vasil'ev, A. V. Kuzmenko, “Representation of the scattering amplitude by a functional integral and quasiclassical asymptotic behavior in quantum mechanics”, Theoret. and Math. Phys., 31:3 (1977), 479–488  mathnet  crossref  mathscinet
    8. V. N. Sushko, “Fermionization of the $(\sin\varphi)_2$ interaction in a box”, Theoret. and Math. Phys., 37:2 (1978), 949–969  mathnet  crossref  mathscinet
    9. V. E. Korepin, “Above-barrier reflection of solitons”, Theoret. and Math. Phys., 34:1 (1978), 1–8  mathnet  crossref
    10. B. M. Barbashov, V. V. Nesterenko, A. M. Chervyakov, “Solitons in some geometrical field theories”, Theoret. and Math. Phys., 40:1 (1979), 572–581  mathnet  crossref  mathscinet  isi
    11. E. K. Sklyanin, L. A. Takhtadzhyan, L. D. Faddeev, “Quantum inverse problem method. I”, Theoret. and Math. Phys., 40:2 (1979), 688–706  mathnet  crossref  mathscinet  isi
    12. V. P. Maslov, G. A. Omel'yanov, “Asymptotic soliton-form solutions of equations with small dispersion”, Russian Math. Surveys, 36:3 (1981), 73–149  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. V. G. Budanov, “Particle in a self-consistent field some exact solutions”, Theoret. and Math. Phys., 49:2 (1981), 979–986  mathnet  crossref  mathscinet  isi
    14. A. N. Leznov, M. V. Saveliev, V. G. Smirnov, “Theory of group representations and integration of nonlinear dynamical systems”, Theoret. and Math. Phys., 48:1 (1981), 565–571  mathnet  crossref  mathscinet  zmath  isi
    15. S. I. Zlatev, V. A. Matveev, G. A. Chechelashvili, “The problem of zero-frequency modes in the quantum theory of solitons”, Theoret. and Math. Phys., 50:3 (1982), 211–217  mathnet  crossref  mathscinet  isi
    16. A. N. Leznov, I. A. Fedoseev, “Explicitly integrable models of quantum field theory with exponential interaction in two-dimensional space”, Theoret. and Math. Phys., 53:3 (1982), 1175–1185  mathnet  crossref  mathscinet  isi
    17. K. A. Sveshnikov, “Covariant perturbation theory in the neighborhood of a classical solution”, Theoret. and Math. Phys., 55:3 (1983), 553–568  mathnet  crossref  mathscinet  isi
    18. V. B. Tverskoi, “Heisenberg fields in the neighborhood of a classical solution”, Theoret. and Math. Phys., 68:3 (1986), 866–873  mathnet  crossref  mathscinet  isi
    19. A. E. Dorokhov, “Covariant quantization in models of extended objects”, Theoret. and Math. Phys., 70:1 (1987), 35–42  mathnet  crossref  isi
    20. Yu. S. Osipov, A. A. Gonchar, S. P. Novikov, V. I. Arnol'd, G. I. Marchuk, P. P. Kulish, V. S. Vladimirov, E. F. Mishchenko, “Lyudvig Dmitrievich Faddeev (on his sixtieth birthday)”, Russian Math. Surveys, 50:3 (1995), 643–659  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    21. D. V. Yur'ev, “Topics in isotopic pairs and their representations. II. A general supercase”, Theoret. and Math. Phys., 111:1 (1997), 511–518  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    22. I. D. Mandzhavidze, A. N. Sisakyan, “Perturbation theory in the neighborhood of extended objects”, Theoret. and Math. Phys., 123:3 (2000), 776–791  mathnet  crossref  crossref  mathscinet  zmath  isi
    23. Manjavidze, J, “Very high multiplicity hadron processes”, Physics Reports-Review Section of Physics Letters, 346:1 (2001), 2  isi
    24. I. D. Mandzhavidze, A. N. Sisakyan, “A Field Theory Description of Constrained Energy-Dissipation Processes”, Theoret. and Math. Phys., 130:2 (2002), 153–197  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    25. Vicedo B., “The method of finite-gap integration in classical and semi-classical string theory”, J. Phys. A: Math. Theor., 44:12 (2011), 124002  crossref  isi
    26. Kwiatkowski G. Leble S., “Quantum Corrections to Sg Equation Solutions and Applications”, Phys. Lett. A, 376:8-9 (2012), 991–995  crossref  isi
    27. Kwiatkowski G. Leble S., “Quantum Corrections to I Center Dot (4) Model Solutions and Applications to Heisenberg Chain Dynamics”, Cent. Eur. J. Phys., 11:7 (2013), 887–893  crossref  isi
    28. Zarmi Ya., “Nonlinear Quantum-Dynamical System Based on the Kadomtsev-Petviashvili II Equation”, J. Math. Phys., 54:6 (2013), 063515  crossref  isi
    29. I. Ya. Aref'eva, V. M. Buchstaber, E. P. Velikhov, A. B. Zhizhchenko, V. E. Zakharov, I. A. Ibragimov, S. V. Kislyakov, V. V. Kozlov, P. P. Kulish, L. N. Lipatov, V. P. Maslov, V. A. Matveev, S. P. Novikov, Yu. S. Osipov, A. M. Polyakov, V. A. Rubakov, M. A. Semenov-Tian-Shansky, Yu. A. Simonov, Ya. G. Sinai, A. A. Slavnov, I. A. Sokolov, L. A. Takhtadzhyan, V. E. Fortov, S. L. Shatashvili, “Ludvig Dmitrievich Faddeev (on his 80th birthday)”, Russian Math. Surveys, 69:6 (2014), 1133–1142  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    30. Kwiatkowski G. Leble S., “Quantum Corrections To Quasi-Periodic Solution of sine-Gordon Model and Periodic Solution of Phi(4) Model”, Physics and Mathematics of Nonlinear Phenomena 2013, Journal of Physics Conference Series, 482, IOP Publishing Ltd, 2014, 012023  crossref  isi
    31. L. A. Takhtajan, A. Yu. Alekseev, I. Ya. Aref'eva, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, S. L. Shatashvili, “Scientific heritage of L. D. Faddeev. Survey of papers”, Russian Math. Surveys, 72:6 (2017), 977–1081  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    32. Alexander Moll, “Exact Bohr–Sommerfeld Conditions for the Quantum Periodic Benjamin–Ono Equation”, SIGMA, 15 (2019), 098, 27 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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