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TMF, 1972, Volume 10, Number 2, Pages 162–181 (Mi tmf2652)  

This article is cited in 35 scientific papers (total in 35 papers)

Oscillator levels of a particle as a consequence of a strong interaction with a field

E. P. Solodovnikova, A. N. Tavkhelidze, O. A. Khrustalev


Abstract: A Bogolyubov transformation is used to separate the motion of a particle that interacts strongly with a scalar field. The effective potential for the particle in this case reduces to an oscillator potential.

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English version:
Theoretical and Mathematical Physics, 1972, 10:2, 105–118

Received: 11.06.1971

Citation: E. P. Solodovnikova, A. N. Tavkhelidze, O. A. Khrustalev, “Oscillator levels of a particle as a consequence of a strong interaction with a field”, TMF, 10:2 (1972), 162–181; Theoret. and Math. Phys., 10:2 (1972), 105–118

Citation in format AMSBIB
\Bibitem{SolTavKhr72}
\by E.~P.~Solodovnikova, A.~N.~Tavkhelidze, O.~A.~Khrustalev
\paper Oscillator levels of a particle as a consequence of a strong interaction with a field
\jour TMF
\yr 1972
\vol 10
\issue 2
\pages 162--181
\mathnet{http://mi.mathnet.ru/tmf2652}
\transl
\jour Theoret. and Math. Phys.
\yr 1972
\vol 10
\issue 2
\pages 105--118
\crossref{https://doi.org/10.1007/BF01090720}


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    This publication is cited in the following articles:
    1. E. P. Solodovnikova, A. N. Tavkhelidze, O. A. Khrustalev, “Bogolyubov transformation in the strong coupling theory. II”, Theoret. and Math. Phys., 11:3 (1972), 537–546  mathnet  crossref
    2. E. P. Solodovnikova, A. N. Tavkhelidze, O. A. Khrustalev, “Bogolyubov transformation in a strong coupling theory. III”, Theoret. and Math. Phys., 12:2 (1972), 731–741  mathnet  crossref
    3. A. A. Arkhipov, N. E. Tyurin, “Scattering problem in the theory of strong coupling”, Theoret. and Math. Phys., 17:1 (1973), 984–990  mathnet  crossref
    4. O. D. Timofeevskaya, N. E. Tyurin, A. V. Shurgaya, “Method of strong coupling in charged scalar theory with two sources”, Theoret. and Math. Phys., 17:1 (1973), 999–1007  mathnet  crossref
    5. N. E. Tyurin, A. V. Shurgaya, “Strong coupling method in fixed-source model”, Theoret. and Math. Phys., 16:2 (1973), 771–782  mathnet  crossref
    6. S. V. Semenov, “Three-body problem in strong coupling theory”, Theoret. and Math. Phys., 18:3 (1974), 251–260  mathnet  crossref
    7. A. N. Tolstenkov, N. E. Tyurin, A. V. Shurgaya, “Rong coupling method in a scalar (3)-symmetric theory”, Theoret. and Math. Phys., 19:2 (1974), 459–464  mathnet  crossref
    8. N. E. Tyurin, O. A. Khrustalev, “Scattering of particles with allowance for an interaction with a quantized scalar field”, Theoret. and Math. Phys., 20:1 (1974), 621–631  mathnet  crossref
    9. R. V. Jolos, V. G. Kartavenko, V. Rybarska, “Bogolyubov's method in the problem of pairing vibrations and the problem of eliminating unphysical states”, Theoret. and Math. Phys., 20:3 (1974), 873–880  mathnet  crossref
    10. E. P. Solodovnikova, A. N. Tavkhelidze, “Two-body problem in adiabatic and strong coupling”, Theoret. and Math. Phys., 21:1 (1974), 935–947  mathnet  crossref
    11. 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
    12. A. V. Shurgaya, “Motion of a nonre lativistic particle with spin in a quantum field with strong coupling”, Theoret. and Math. Phys., 28:2 (1976), 745–750  mathnet  crossref
    13. L. I. Komarov, E. V. Krylov, Nguyen Fyog Lun, I. D. Feranchuk, “Bogolyubov transformation in the theory of strong coupling of a heavy particle to a scalar field”, Theoret. and Math. Phys., 32:2 (1977), 730–736  mathnet  crossref
    14. A. V. Razumov, “Bogolyubov transformation and quantization of solitons”, Theoret. and Math. Phys., 30:1 (1977), 10–16  mathnet  crossref  mathscinet
    15. A. I. Ivanov, O. A. Ponomarev, “Investigation of the Fröhlich model by the method of functional derivatives”, Theoret. and Math. Phys., 30:3 (1977), 246–255  mathnet  crossref  mathscinet
    16. A. V. Shurgaya, “Nonrelativistic model of the interaction of a scalar particle with a quantized field”, Theoret. and Math. Phys., 34:2 (1978), 169–173  mathnet  crossref
    17. A. V. Razumov, A. Yu. Taranov, “Scattering on a nonrelativistic particle in strong-coupling theory”, Theoret. and Math. Phys., 35:3 (1978), 480–487  mathnet  crossref  mathscinet
    18. A. I. Ivanov, G. S. Lomakin, O. A. Ponomarev, “Investigation of systems with quadratic interaction by the method of functional derivatives”, Theoret. and Math. Phys., 41:2 (1979), 1020–1028  mathnet  crossref  mathscinet  isi
    19. A. V. Razumov, A. Yu. Taranov, “Dipole interaction of an oscillator with scalar field”, Theoret. and Math. Phys., 38:3 (1979), 235–241  mathnet  crossref  mathscinet
    20. Sh. I. Vashakidze, V. A. Matveev, “Bogolyubov transformation in the problem of capture of a massive particle by a quantum field”, Theoret. and Math. Phys., 45:3 (1980), 1069–1077  mathnet  crossref  mathscinet  isi
    21. A. V. Shurgaya, “The method of collective variables and the generalized Hamiltonian formalism”, Theoret. and Math. Phys., 45:1 (1980), 873–879  mathnet  crossref  mathscinet  isi
    22. 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
    23. 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
    24. V. G. Bornyakov, “Strong coupling method in a symmetric scalar theory with two sources”, Theoret. and Math. Phys., 51:2 (1982), 476–483  mathnet  crossref  isi
    25. A. V. Razumov, A. Yu. Taranov, “Collective coordinates on symplectic manifolds”, Theoret. and Math. Phys., 52:1 (1982), 641–647  mathnet  crossref  mathscinet  zmath  isi
    26. 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
    27. A. V. Shurgaya, “The method of collective variables in relativistic theory”, Theoret. and Math. Phys., 57:3 (1983), 1216–1225  mathnet  crossref  isi
    28. S. I. Zlatev, V. A. Matveev, “The problem of infrared divergences in soliton quantization”, Theoret. and Math. Phys., 62:1 (1985), 31–42  mathnet  crossref  isi
    29. A. A. Torotadze, A. V. Shurgaya, “Two-dimensional model of the interaction of a nonrelativistic particle with scalar mesons in the strong-coupling limit”, Theoret. and Math. Phys., 76:2 (1988), 826–833  mathnet  crossref  isi
    30. Theoret. and Math. Phys., 93:3 (1992), 1345–1360  mathnet  crossref  isi
    31. K. A. Sveshnikov, “Nonclassical analogs of solitons in quantum field theory”, Theoret. and Math. Phys., 94:1 (1993), 39–47  mathnet  crossref  mathscinet  zmath  isi
    32. O. A. Khrustalev, M. V. Chichikina, “Bogoliubov group variables in the relativistic quantum field theory”, Theoret. and Math. Phys., 111:2 (1997), 583–591  mathnet  crossref  crossref  mathscinet  zmath  isi
    33. P. K. Silaev, O. A. Khrustalev, “Double-periodic solutions in an essentially nonlinear one-dimensional field model”, Theoret. and Math. Phys., 117:2 (1998), 1345–1350  mathnet  crossref  crossref  zmath  isi
    34. E. Yu. Spirina, O. A. Khrustalev, M. V. Chichikina, “Nonstationary polaron”, Theoret. and Math. Phys., 122:3 (2000), 347–354  mathnet  crossref  crossref  mathscinet  zmath  isi
    35. Jafarov R.G. Agham-Alieva L.A. Agha-Kishieva P.E. Rahim-zade S.G. Mamedova S.N. Mutallimov M.M., “Problem of the Landau Poles in Quantum Field Theory: from N. N. Bogolyubov to the Present Day”, Russ. Phys. J., 59:11 (2017), 1971–1980  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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