Quantum Integrable Systems

Quantum Integrable Systems

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The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the more recent advances. This book presents and clarifies the developments of the last ten years in quantum integrable systems. After a preliminary discussion of the fundamentals of classical nonlinear integrable systems, the authors explore the quantum domain. Their approach emphasizes physical systems and the use of concrete examples, and they take care to establish the relationship between new and older methods. The presentation includes the first comprehensive discussion of the quantum Backlund transformation Q-operator and various techniques related to algebraic Bethe Ansatz that are not available elsewhere in book form. In Quantum Integrable Systems, researchers active in the field have an up-to-date source for recent advances and new techniques, and nonspecialists finally have an accessible introduction to the concepts and basic tools they need to explore and exploit the wide-ranging applicability of the subject.
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Product details

  • Paperback | 424 pages
  • 238.8 x 316.5 x 22.6mm | 589.68g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • 1000 equations; 36 Illustrations, black and white
  • 1584883804
  • 9781584883807
  • 2,543,482

Table of contents

NONLINEAR SYSTEMS AND CLASSICAL ISTIntroductionDefinition of IntegrabilityLax Pair TechniqueInverse Scattering TransformHamiltonian StructureCOORDINATE BETHE ANSATZIntroductionNonlinear Systems and the CBAFermionic SystemBoundary Condition in Bethe AnsatzHeisenberg Spin ChainSpin of the Bethe Ansatz StateOther Integrable ModelsYANG-BAXTER EQUATIONIntroductionGeneral DescriptionFactorized ScatteringBaxter's Star Triangle RelationVertex ModelsReflection Equation AlgebraCONTINUOUS INTEGRABLE SYSTEMSIntroductionQuantum Continuous Integrable SystemsConserved QuantitiesNonultralocal systems and the YBEOperator Product Expansion and YBEFinite Boundary ConditionsModified Classical Yang-Baxter EquationALGEBRAIC BETHE ANSATZIntroductionDiscrete Self Trapping ModelAsymmetric XXZ Model in a Magnetic FieldAnalytical Bethe AnsatzOff-Shell Bethe AnsatzNested Bethe AnsatzFusion ProcedureFusion Procedure for Open chainsFusion Procedure for Transfer MatricesApplication of Fusion ProcedureINTEGRABLE LONG-RANGE MODELSIntroductionLong-Range Models from the ABASymmetry TransformationCalogero-Moser ModelsSEPARATION OF VARIABLESIntroductionHamilton-Jacobi EquationSklyanin's Method for SoVGoryachev-Chaplygin TopQuantum Case and the Role of Lie AlgebraBi-Hamiltonian Structure and SoVSoV for GCM ModelSoV and Boundary ConditionsBAECKLUND TRANSFORMATIONSIntroductionPermutability TheoremBacklund Transformations and Classical Inverse ScatteringBacklund Transformations from Riccati EquationDarboux Backlund TransformationsThe Exponential LatticeCanonical TransformationsGroup Property of Backlund TransformationsRecent Developments in Backlund Transformation TheorySklyanin's Formalism for Canonical BacklundTransformationsExtended Phase Space MethodQuantization of Backlund TransformationsMethod of Projection OperatorsQUANTUM GLM EQUATIONIntroductionQuantum GLM EquationQuantum Floquet FunctionExact QuantizationQuantum GLM Equation in a Continuous SystemBound States and an Alternative ApproachAPPENDICESDirect Product CalculusGrassman AlgebraBethe Ansatz EquationAKNS ProblemBIBLIOGRAPHYINDEX
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