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Fifty Years Of Mathematical Physics: Selected Works Of Ludwig Faddeev [Kietas viršelis]

Edited by (Nankai Univ, China), Edited by (Nordita, Sweden)
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This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.
Foreword v
C. N. Yang
PART 1 Scattering Theory
1(42)
[ 1-1] (with V. S. Buslaev) Formulas for traces for a singular Sturm-Liouville differential operator, Sov. Math. Dokl. 1 (1960) 451--454 (Engl, transl.)
3(4)
[ 1-2] On the Friedrichs model in the theory of perturbations of a continuous spectrum, Amer. Math. Soc. Transl., II. Ser. 62 (1967) 177--203 (Engl, transl.)
7(27)
[ 1-3] Increasing solutions of the Schrodinger equation, Sov. Phys. Dokl. 10 (1966) 1033--1035 (Engl, transl.)
34(3)
[ 1-4] Scattering theory for a three-particle system, Sov. Phys. JETP 12 (1961) 1014 1019 (Engl, transl.)
37(6)
PART 2 Automorphic Functions
43(88)
[ 2-1] Expansion in eigenfunctions of the Laplace operator on the fundamental domain of a discrete group on the Lobacevskii plane, Trans. Moscow Math. Soc. 17 (1967) 357-386 (Engl, transl.)
45(30)
[ 2-2] (with B. S. Pavlov) Scattering theory and automorphic functions, J. Sov. Math. 3 (1975) 522--548 (Engl, transl.)
75(27)
[ 2-3] (with A. B. Venkov and V. L. Kalinin) A nonarithmetic derivation of the Selberg trace formula, J. Sov. Math. 8 (1977) 171--199 (Engl, transl.)
102(29)
PART 3 Field Theory
131(144)
[ 3-1] (with F. A. Berezin) A remark on Schrodinger's equation with a singular potential, Sov. Math. Dokl. 2 (1961) 372--375 (Engl, transl.)
133(4)
[ 3-2] Distinction between interaction and scattering effects in perturbation theory, Sov. Phys. Dokl. 8 (1964) 881--883 (Engl, transl.)
137(3)
[ 3-3] (with V. N. Popov) An approach to the theory of the low-temperature Bose gas, Sov. Phys. JETP 20 (1965) 890-893 (Engl, transl.)
140(4)
[ 3-4] (with P. P. Kulish) Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4 (1970) 745-757 (Engl, transl.)
144(13)
[ 3-5] (with V. N. Popov) Feynman diagrams for the Yang-Mills field, Phys. Lett. B 25 (1967) 29--30 (Engl, transl.)
157(2)
[ 3-6] (with L. A. Takhtajan) Liouville model on the lattice, in Lecture Notes in Phys., Vol. 246 (Springer, 1986), pp. 166--179
159(14)
[ 3-7] (with R. Jackiw) Hamiltonian reduction of unconstrained and constrained systems, Phys. Rev. Lett. 60 (1988) 1692--1694
173(3)
[ 3-8] (with A. Alekseev and S. Shatashvili) Quantization of symplectic orbits of compact Lie groups by means of the functional integral, J. Geom. Phys. 5 (1989) 391--406
176(16)
[ 3-9] (with A. Yu. Alekseev) (T*G)tm. A toy model for conformal field theory, Commun. Math. Phys. 141 (1991) 413--422
192(10)
[ 3-10] (with A. Alekseev, M. Semenov-Tian-Shansky and A. Volkov) The unravelling of the quantum group structure in the WZNW theory, preprint CERN-TH-5981/91 (1991)
202(16)
[ 3-11] (with A. Yu. Alekseev) An involution and dynamics for the q-deformed quantum top, J. Math. Sci. 77 (1995) 3137--3145 (Engl, transl.)
218(9)
[ 3-12] Quantum symmetry in conformal field theory by Hamiltonian methods, in New Symmetry Principles in Quantum Field Theory (NATO Adv. Sci. Inst. Ser. B Phys., Vol. 295) (Plenum, 1992), pp. 159--175
227(17)
[ 3-13] (with A. Yu. Volkov) Abelian current algebra and the Virasoro algebra on the lattice, Phys. Lett. B 315 (1993) 311--318
244(8)
[ 3-14] (with A. Yu. Volkov) Hirota equation as an example of an integrable symplectic map, Lett. Math. Phys. 32 (1994) 125-135
252(11)
[ 3-15] (with A. Yu. Volkov) Discrete evolution for the zero modes of the quantum Liouville model, J. Phys. A 41 (2008) 194008 (Engl, transl.)
263(12)
PART 4 Theory of Solitons
275(178)
[ 4-1] (with V. E. Zakharov) Korteweg-de Vries equation: A completely integrable Hamiltonian system, Fund. Anal Appl. 5 (1971) 280-287 (Engl, transl.)
277(8)
[ 4-2] Some comments on the many-dimensional solitons, Lett. Math. Phys. 1 (1976) 289-293
285(5)
[ 4-3] (with E. K. Sklyanin) Quantum-mechanical approach to completely integrable field theory models, Sov. Phys. Dokl. 23 (1978) 902-904 (Engl, transl.)
290(3)
[ 4-4] (with L. A. Takhtajan) What is the spin of a spin wave?, Phys. Lett. A 85 (1981) 375-377
293(3)
[ 4-5] (with L. A. Takhtadzhyan) Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model, J. Sov. Math. 24 (1984) 241--267 (Engl, transl.)
296(27)
[ 4-6] (with N. Yu. Reshetikhin) Hamiltonian structures for integrable models of field theory, Theor. Math. Phys. 56 (1983) 847--862 (Engl, transl.)
323(16)
[ 4-7] (with V. O. Tarasov and L. A. Takhtadzhyan), Local Hamiltonians for integrable quantum models on a lattice, Theor. Math. Phys. 57 (1984) 1059--1073 (Engl, transl.)
339(15)
[ 4-8] Instructive history of the quantum inverse scattering method, Acta Appl. Math. 39 (1995) 69--84
354(16)
[ 4-9] How the algebraic Bethe Ansatz works for integrable models, in Symetries Quantiques (Proc. of Les Houches, Session LXIV, 1995) (North-Holland, 1998), pp. 149--219
370(70)
[ 4-10] (with G. P. Korchemsky), High energy QCD as a completely integrable model, Phys. Lett. B 342 (1995) 311--322
440(13)
PART 5 Quantum Groups
453(78)
[ 5-1] (with N. Reshetikhin and L. Takhtajan) Quantum groups, in Braid Group, Knot Theory and Statistical Mechanics (World Scientific, 1989), pp. 97--110
455(14)
[ 5-2] (with N. Yu. Reshetikhin and L. A. Takhtadzhyan) Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1 (1990) 193-225 (Engl, transl.)
469(33)
[ 5-3] (with R. M. Kashaev) Quantum dilogarithm, Mod. Phys. Lett. A 9 (1994) 427--434
502(8)
[ 5-4] (with P. N. Pyatov) The differential calculus on quantum linear groups, in Contemporary Mathematical Physics (AMS Transl. Ser. 2, Vol. 175) (Amer. Math. Soc, 1996), pp. 35--47
510(13)
[ 5-5] Modular double of a quantum group, Math. Phys. Stud. 21 (2000) 149--156
523(8)
PART 6 Knots
531(16)
[ 6-1] (with A. J. Niemi) Stable knot-like structures in classical field theory, Nature 387 (May 1997) 58--61
533(4)
[ 6-2] Knotted solitons, in Proceedings of the International Congress of Mathematicians 2002, Vol. I, pp. 235--244
537(10)
PART 7 General Questions
547(10)
[ 7-1] Modern mathematical physics: What it should be, in Mathematical Physics 2000 (Imperial College Press, 2000), pp. 1--8
549(8)
List of Publications 557