Fifty Years Of Mathematical Physics: Selected Works Of Ludwig Faddeev

by Mo-lin Ge, Antti Niemi

Overview

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.

Product Details

ISBN-13:	9789813109339
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	04/16/2016
Series:	World Scientific Series In 21st Century Mathematics , #2
Pages:	596
Product dimensions:	6.90(w) x 10.00(h) x 1.20(d)

Table of Contents

Foreword C. N. Yang v

Part 1 Scattering Theory 1

1-1 Formulas for traces for a singular Sturm-Liouville differential operator, Sov. Math. Dokl 1 (1960) 451-454 (Engl. transl.) V. S. Buslaev 3

1-2 On the Friedrichs model in the theory of perturbations of a continuous spectrum, Amer. Math. Soc. Transl., II. Ser. 82 (1967) 177-203 (Engl. transl.) 7

1-3 Increasing solutions of the Schrbdinger equation, Sov. Phys. Dokl. 10 (1966) 1033-1035 (Engl. transl.) 34

1-4 Scattering theory for a three-particle system, Sov. Phys. JETP 12 (1961) 1014 1019 (Engl. transl.) 37

Part 2 Automorphic Functions 43

2-1 Expansion in eigenfunctions of the Laplace operator on the fundamental domain of a discrete group on the Lobacevskiï plane, Trans. Moscow Math. Soc. 17 (1967) 357-386 (Engl. transl.) 45

2-2 Scattering theory and automorphic functions. J. Sov. Math. 3 (1975) 522-548 (Engl. transl.) B. S. Pavlov 75

2-3 A nonarithmetic derivation of the Selberg trace formula, J. Sov. Math. 8 (1977) 171-199 (Engl. transl.) A. B. Venkov V. L. Kalinin 102

Part 3 Field Theory 131

3-1 A remark on Sehrödinger's equation with a singular potential, Sov. Math. Dokl. 2 (1961) 372 375 (Engl. transl.) F. A. Berezin) 133

3-2 Distinction between interaction and scattering effects in perturbation theory, Sov. Phys. Dokl. 8 (1964) 881-883 (Engl. transl.) 137

3-3 An approach to the theory of the low-temperature Bose gas, Sov. Phys. JETP 20 (1965) 890- 893 (Engl. transl.) V. N. Popov)140

3-4 Asymptotic conditions and infrared divergences in quantum electrodynamics, Theor. Math. Phys. 4 (1970) 745-757 (Engl. transl.) P. P. Kulish) 144

3-5 Feynman diagrams for the Yang-Mills field, Phys. Lett. B 25 (1967) 29-30 (Engl. transl.) V. N. Popov 157

3-6 Liouville model on the lattice, in Lecture Notes in Phys., Vol. 246 (Springer. 1986), pp. 166-179 L. A. Takhtajan) 159

3-7 Hamiltonian reduction of unconstrained and constrained systems. Phys. Rev. Lett. 60 (1988) 1692-1694 R. Jackiw 173

3-8 Quantization of symplectic orbits of compact Lie groups by means of the functional integral, J. Geom, Phys. 5 (1989) 391-406 A. Alekseev S. Shatashvili 176

3-9 (T*G)_t: A toy model for conformal field theory, Commun. Math. Phys. 141 (1991)413-422 A. Yu. Alekseev 192

3-10 The unravelling of the quantum group structure in the WZNW theory, preprint CERN-TH-5981/91 (.1991) A. Alekseev M. Semenov-Tian-Shansky A. Volkov 202

3-11 An involution and dynamics for the q-deformed quantum top, J. Math, Sci. 77 (1995) 3137-3145 (Engl. transl.) A. Yu. Alekseev 218

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

3-13 Abelian current algebra and the Virasoro algebra on the lattice, Phys. Lett. B 315 (1993) 311-318 A. Yu. Volkov 244

3-14 Hirota equation as an example of an integrable symplectic map, Lett. Math. Phys. 32 (1994) 125-135 A. Yu. Volkov 252

3-15 Discrete evolution for the zero modes of the quantum Liouville model, J. Phys. A 41 (2008) 194008 (Engl. transl.) A. Yu. Volkov 263

Part 4 Theory of Solitons 275

4-1 Korteweg-de Vries equation: A completely integrable Hamiltonian system, Fund. Anal. Appl. 5 (1971) 280-287 (Engl. transl.) V. E. Zakharov 277

4-2 Some comments on the many-dimensional solitons, Lett. Math. Phys. 1 (1976) 289-293 285

4-3 Quantum-mechanical approach to completely integrable field theory models, Sov. Phys. Dokl 23 (1978) 902-904 (Engl. transl.) E. K. Sklyanin 290

4-4 What is the spin of a spin wave?, Phys. Lett. A 85 (1981) 375-377 L. A. Takhtajan 293

4-5 Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model, J. Sov. Math. 24 (1984) 241-267 (Engl. transl.) L. A. Takhtadzhyau 296

4-6 Hamiltonian structures for integrable models of field, theory, Theor. Math. Phys. 56 (1983) 847-862 (Engl. transl.) N. Yu. Reshetikhin 323

4-7 Local Hamiltonians for integrable quantum models on a lattice, Theor. Math. Phys. 57 (1984) 1059-1073 (Engl. transl.) V. O. Tarasov L. A. Takhtadzhyan 339

4-8 Instructive history of the quantum inverse scattering method, Acta Appl. Math. 39 (1995) 69 84 354

4-9 How the algebraic Bethe Ansatz works for integrable models, in Symétries Quantiques (Proc. of Les Houches, Session LXIV, 1995) (North-Holland, 1998), pp. 149-219 370

4-10 High energy QCD as a completely integrable model, Phys. Lett. B 342 (1995) 311-322 G. P. Korchemsky 440

Part 5 Quantum Groups 453

5-1 Quantum groups, in Braid Group, Knot Theory and Statistical Mechanics (World Scientific, 1989), pp. 97-110 N. Reshetikhin L. Takhtajan 455

5-2 Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1 (1990) 193-225 (Engl. transl.) N. Yu. Reshetikhin L. A. Takhtadzhyan 469

5-3 Quantum dilogarithm. Mod. Phys. Lett. A 9 (1994) 427-434 R. M. Kashaev 502

5-4 The differential calculus on quantum linear groups, in Con- temporary Mathematical Physics (AMS Transl. Ser. 2, Vol. 175) (Amer. Math. Soc., 1996), pp. 35-47 P. N. Pyatov 510

5-5 Modular double of a quantum group, Math. Phys. Stud. 21 (2000) 149-156 523

Part 6 Knots 531

6-1 Stable knot-like structures in classical field theory, Nature 387 (May 1997) 58 -61 A. J. Niemi 533

6-2 Knotted solitons, in Proceedings of the International Congress of Mathematicians 2002, Vol. I, pp. 235- 244 537

Part 7 General Questions 547

7-1 Modern mathematical physics: What it should be, in Mathematical Physics 2000 (Imperial College Press, 2000), pp. 1-8 549

List of Publications 557