Scientific heritage of L.D. Faddeev. Survey of papers

DOI10.1070/RM9799zbMath1396.81008OpenAlexW2789254000WikidataQ57532692 ScholiaQ57532692MaRDI QIDQ4581624

Anton Yu. Alekseev, L. A. Takhtadzhyan, Fedor A. Smirnov, Irina Ya. Aref'eva, Michaael A. Semenov-Tian-Shansky, Samson L. Shatashvili, Evgueni K. Sklyanin

Publication date: 20 August 2018

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm9799

zbMATH Keywords

Schrödinger operatorYang-Baxter equationquantum groupsscattering theoryKorteweg-de Vries equationeigenfunction expansionalgebraic Bethe ansatzcomplete integrabilityinverse scattering methodinverse scattering problemquantum anomaliesquantum dilogarithmFaddeev-Popov ghostsquantization of gauge fieldsquantum inverse problem method

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) History of mathematics in the 20th century (01A60) History of quantum theory (81-03) Model quantum field theories (81T10) KdV equations (Korteweg-de Vries equations) (35Q53) Biographies, obituaries, personalia, bibliographies (01A70) Scattering theory for PDEs (35P25) Yang-Mills and other gauge theories in quantum field theory (81T13) Quantization in field theory; cohomological methods (81T70) Path integrals in quantum mechanics (81S40) Anomalies in quantum field theory (81T50) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse scattering problems in quantum theory (81U40) Schrödinger operator, Schrödinger equation (35J10) Exactly solvable models; Bethe ansatz (82B23) Geometry of quantum groups (58B32) Yang-Mills and other gauge theories in mechanics of particles and systems (70S15) Determinants and determinant bundles, analytic torsion (58J52) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Exactly solvable dynamic models in time-dependent statistical mechanics (82C23) Yang-Baxter equations (16T25)

Related Items

Etudes of the resolvent ⋮ Preface: Introduction to special issue: In memory of Ludwig Faddeev ⋮ Exact Bohr-Sommerfeld conditions for the quantum periodic Benjamin-Ono equation ⋮ Geometry and physics: An overview

Cites Work

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• Abelian current algebra and the Virasoro algebra on the lattice
• Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model
• On the exchange matrix for WZNW model
• Quantization of symplectic orbits of compact Lie groups by means of the functional integral
• Quantum inverse problem method. I
• Discrete series of representations for the modular double of the quantum group \(U_q (sl(2, \mathbb R))\)
• Notes on divergences and dimensional transmutation in Yang-Mills theory
• Some algebraic structures connected with the Yang-Baxter equation
• \((T^*G)_ t\): a toy model for conformal field theory
• Hidden quantum groups inside Kac-Moody algebras
• Representations of canonical commutation relations in the limit of an infinite volume
• Essentially nonlinear one-dimensional model of classical field theory
• Reduction of symplectic manifolds with symmetry
• Inverse problem of quantum scattering theory. II
• The Hamiltonian system connected with the equation u//(xi,nu)+sin u=0
• Hirota equation as an example of an integrable symplectic map
• Instructive history of the quantum inverse scattering method
• Discrete Heisenberg-Weyl group and modular group
• The Feynman integral for singular Lagrangians
• Partition function of the eight-vertex lattice model
• Korteweg-de Vries equation: a completely integrable Hamiltonian system
• ALGEBRAIC ASPECTS OF THE BETHE ANSATZ
• Exactly renormalizable model in the quantum theory of fields
• Energy corrections and persistent perturbation effects in continuous spectra
• Generalized Hamiltonian dynamics
• Clothed particle operators in simple models of quantum field theory
• Method for Solving the Korteweg-deVries Equation
• Conservation of Isotopic Spin and Isotopic Gauge Invariance
• ON THE SINGULAR SPECTRUM IN A SYSTEM OF THREE PARTICLES
• Scattering Theory for Automorphic Functions. (AM-87)
• Inverse scattering on the line
• QUANTUM DILOGARITHM
• Strongly coupled quantum discrete Liouville theory: II. Geometric interpretation of the evolution operator
• Two-Dimensional Integrable Models in Quantum Field Theory
• The spectral theory of a functional-difference operator in conformal field theory
• Algebraic Lessons from the Theory of Quantum Integrable Models
• Integrals of nonlinear equations of evolution and solitary waves
• Asymptotic conditions and infrared divergences in quantum electrodynamics
• Note on the Radiation Field of the Electron
• Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality

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