Quantum version of the method of inverse scattering problem
Tóm tắt
Từ khóa
Tài liệu tham khảo
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: Method of the Inverse Problem [in Russian], Nauka, Moscow (1980).
C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, ?Method for solving the Korteweg-de Vries equation,? Phys. Rev. Lett.,19, 1095?1097 (1967).
P. D. Lax, ?Integrals of nonlinear evolutional equations and isolated waves,? Matematika (collection of translations of foreign papers),13, No. 5, 128?150 (1967).
V. E. Zakharov and L. D. Faddeev, ?Korteweg-de Vries equation ?completely integrable Hamiltonian system,? Funkts. Anal. Prilozhen.,5, No. 4, 18?27 (1971).
H. Bethe, ?Zur Theorie der Metalle. I. Eigenwerte und Eigenfunctionen der linearen Atomkette,? Z. Phys.,71, 205?226 (1931).
L. Onsager, ?Crystal statistics. I. A two-dimensional model with an order-disorder transition,? Phys. Rev.,65 (1944).
R. J. Baxter, ?Partition function of the eight-vertex lattice model,? Ann. Phys.,70, No. 1, 193?288 (1972).
V. E. Zahkarov, L. A. Takhtadzhyan, and L. D. Faddeev, ?Complete description of solutions of the ?sin-Gordon? equation,? Dokl. Akad. Nauk SSSR,219, No. 6, 1334?1337 (1974).
V. E. Zakharov and A. V. Mikhailov, ?Relativistically invariant two-dimensional models of the theory of fields, integrable by the method of the inverse problem,? Zh. Eksp. Teor. Fiz.,74, No. 6, 1953?1973 (1978).
P. P. Kulish, S. V. Manakov, and L. D. Faddeev, ?Comparison of exact quantum and quasiclassical answers for the nonlinear Schrödinger equation,? Teor. Mat. Fiz.,28, No. 1, 38?45 (1976).
L. D. Faddeev and V. E. Korepin, ?Quantum theory of solitons,? Phys. Reports,42C, No. 1, 1?87 (1978).
E. K. Sklyanin and L. D. Faddeev, ?Quantum mechanical approach to completely integrable models of field theory,? Dokl. Akad. Nauk SSSR,243, No. 6, 1430?1433 (1978).
E. K. Sklyanin, ?Method of the inverse scattering problem and quantum nonlinear Schrödinger equation,? Dokl. Akad. Nauk SSSR,244, No. 6, 1337?1341 (1978).
E. K. Sklyanin, ?Quantum version of the method of the inverse scattering problem,? Candidates Dissertation, Leningrad Branch of the Mathematics Institute (1980).
L. D. Faddeev, ?Quantum completely integrable models of field theory,? in: Problems of Quantum Field Theory (Memoirs of the International Conference on Nonlocal Field Theories, Alushta, 1979) [in Russian], Dubna (1979), pp. 249?299.
E. K. Sklyanin, L. A. Takhtadzhyan, and L. D. Faddeev, ?Quantum method of the inverse problem I,? Teor. Mat. Fiz.,40, No. 2, 194?220 (1979).
P. P. Kulish and E. K. Sklyanin, ?Quantum inverse scattering method and the Heisenberg ferromagnet,? Phys. Lett. A,70, Nos. 5?6, 461?463 (1979).
L. A. Takhtadzhyan and L. D. Faddeev, ?Quantum method of the inverse problem and the XYZ-model of Heisenberg,? Usp. Mat. Nauk,34, No. 5, 13?63 (1979).
P. P. Kulish, ?Generalized Bethe Ansatz and the quantum method of the inverse problem,? Preprint Leningrad Branch of the Mathematics Institute P-3-79, Leningrad (1979).
P. P. Kulish and N. Yu. Reshetikhin, ?Generalized Heisenberg ferromagnet and the Groos-Neveu model,? Preprint Leningrad Branch of the Mathematics Institute E-4-79, Leningrad (1979).
H. B. Thacker and D. Wilkinson, ?The inverse scattering transform as an operator method in quantum field theory,? Phys. Rev.,D19, No. 12, 3660?3665 (1979).
D. B. Creamer, H. B. Thacker, and D. Wilkinson, ?Gelfand-Levitan method for operator fields,? Preprint Fermilab-Pub-79/75-THY, September, 1979.
D. B. Creamer, H. B. Thacker, and D. Wilkinson, ?Quantum Gelfand-Levitan method as a generalized Jordan-Wigner transformation,? Fermilab-Pub-80/17-THY, January, 1980.
D. B. Creamer, H. B. Thacker, and D. Wilkinson, ?Statistical mechanics of an exactly integrable system,? Fermilab-Pub-80/25-THY, February, 1980.
J. Hönerkamp, P. Weber, and A. Wiesler, ?On the connection between the inverse transform method and the exact quantum eigenstates,? Nucl. Phys.,B152, No. 2, 266 (1979).
A. Wiesler, ?Rigorous proof of ?Bethe's hypothesis? from inverse scattering transformation,? Preprint. Univ. Freiburg THEP 79/8, October, 1979.
H. Grosse, ?On the construction of Möller operators for the nonlinear Schrödinger equation,? Phys. Lett.,86B, Nos. 3?4, 267?271 (1979).
E. K. Sklyanin, ?On complete integrability of the Landau-Lifshits equation,? Preprint, Leningrad Branch of the Mathematics Institute, E-3-79, Leningrad (1979).
V. E. Zakharov and S. V. Manakov, ?Complete integrability of the nonlinear Schrödinger equation,? Teor. Mat. Fiz.,19, No. 3, 332?343 (1974).
V. E. Zakharov and A. B. Shabat, ?Exact theory of two-dimensional self-focusing and one-dimensional automodulation of waves in nonlinear media,? Zh. Eksp. Teor. Fiz.,61, No. 1, 118?134 (1971).
L. A. Takhtadzhyan, ?Hamiltonian systems connected with Dirac's equation,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,37, 66?76 (1973).
F. A. Berezin, G. P. Pokhil, and V. M. Finkel'berg, ?Schrödinger's equation for systems of one-dimensional particles with pointwise interactions,? Vestn. Mosk. Gos. Univ., Ser. Mat., Mekh., No. 1, 21?28 (1964).
J. B. McGuire, ?Study of exactly soluble one-dimensional N-body problem,? J. Math. Phys.,5, No. 5, 622 (1964).
I. M. Gel'fand and L. A. Dikii, ?Resolvent and Hamiltonian systems,? Funkts. Anal.,11, No. 2, 11?27 (1977).
F. A. Berezin, Method of Secondary Quantization [in Russian], Nauka, Moscow (1965).
A. S. Shvarts, Mathematical Foundations of Quantum Field Theory [in Russian], Atomizdat, Moscow (1975).
A. A. Tsvetkov, ?Integrals of motion of a system of bosons with pointwise interactions,? Vestn. Mosk. Gos. Univ., Ser. Mat., Mekh., No. 4, 61?69 (1977).
F. A. Berezin, ?Quantization,? Izv. Akad. Nauk SSSR, Ser. Mat.,38, No. 5, 1116?1175 (1974).
F. A. Berezin, ?Wick and anti-Wick symbols of operators,? Mat. Sb.,86 (128), No. 4 (12), 578?610 (1971).
Yu. S. Tyupkin, V. A. Fateev, and A. S. Shvarts, ?Connection of particle-similar solutions of classical equations with quantum particles,? Yad. Fiz.,22, No. 3, 622?631 (1975).