Lie Theory and Its Applications in Physics [electronic resource] : Varna, Bulgaria, June 2013 /
Dobrev, V. K.,author.
Dobrev, Vladimir.editor.
Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear PDE, special functions, and others. Furthermore, the necessary tools from functional analysis and number theory are included. This is a big interdisciplinary and interrelated field. Samples of these fresh trends are presented in this volume, based on contributions from the Workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2013. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists and researchers in the field of Lie Theory.
Description based upon print version of record.
Preface; Acknowledgments; Contents; List of Participants; Part I Plenary Talks; Revisiting Trace Anomalies in Chiral Theories; 1 Introduction; 2 One-Loop Trace Anomaly in Chiral Theories; 3 Pontryagin Density and Supersymmetry; 3.1 Minimal Supergravity; 3.2 Other Nonminimal Supergravities; References; Complete T-Dualization of a String in a Weakly Curved Background; 1 Bosonic String in the Weakly Curved Background; 2 Partial T-Dualization; 2.1 The Partially T-Dualized Action; 3 The Total T-Dualization of the Initial Action; References; Modular Double of the Quantum Group SLq(2,R)
1 Definitions2 Weyl Pair; 3 Explicit Realization; 4 Representation πs; 5 Quantum Dilogarithm; 6 Decomposition of  πs1 πs2 ; References; Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance; 1 Introduction; 2 Logarithmic Representations; 2.1 Schrödinger Algebra; 2.2 Conformal Galilean Algebra; 2.3 Exotic Conformal Galilean Algebra; 2.4 Ageing Algebra; 2.5 Discussion; 3 Large-Distance Behaviour and Causality; 3.1 Schrödinger Algebra; 3.2 Conformal Galilean Algebra; 3.3 Discussion; References; New Type of N=4 Supersymmetric Mechanics; 1 Introduction
2 SU(2|1) Superspace2.1 Deformed Superspace; 2.2 Covariant Derivatives; 3 The Supermultiplet (1, 4, 3); 4 The (1, 4, 3) Oscillator Model; 4.1 Wave Functions; 4.2 Spectrum and SU(2|1) Representations; 5 The Supermultiplet (2,4,2); 5.1 Chiral Subspaces; 5.2 SU(2|1) Invariant Lagrangian; 5.3 Quantum Generators; 6 Simplified Model on a Complex Plane; 6.1 Wave Functions and Spectrum; 7 Summary and Outlook; References; Vector-Valued Covariant Differential Operators for the Möbius Transformation; 1 A Family of Vector-Valued Functional Identities; 2 Three Equivalent Formulations
2.1 Covariance of SL(2,R) for Vector-Valued Functions2.2 Conformally Covariant Differential Operators; 2.3 Branching Laws of Verma Modules; 3 Rankin-Cohen Brackets; 3.1 Homogeneous Line Bundles over P1C; 3.2 Rankin-Cohen Bidifferential Operator; 4 Holomorphic Trick; 4.1 Restriction to a Totally Real Submanifold; 4.2 Identities of Jacobi Polynomials; 4.3 Proof of Theorem A; 4.4 Scalar-Valued Case; References; Semi-classical Scalar Products in the Generalised SU(2) Model; 1 Introduction; 2 Algebraic Bethe Ansatz for Integrable Models with su(2) R-Matrix
3 Determinant Formulas for the Inner Product4 Field Theory of the Inner Product; 4.1 The A-Functional in Terms of Free Fermions; 4.2 Bosonic Theory and Coulomb Gas; 4.3 The Thermodynamical Limit; 4.4 Coarse-Graining; 4.5 The First Two Orders of the Semi-classical Expansion; 5 Discussion; References; Weak Poisson Structures on Infinite Dimensional Manifolds and Hamiltonian Actions; 1 Introduction; 2 Infinite Dimensional Poisson Manifolds; 2.1 Locally Convex Manifolds; 2.2 Weak Poisson Manifolds; 2.3 Examples of Weak Poisson Manifolds; 2.4 Poisson Maps; 3 Momentum Maps
3.1 Momentum Maps as Poisson Morphisms
Includes bibliographical references.
Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear PDE, special functions, and others. Furthermore, the necessary tools from functional analysis and number theory are included. This is a big interdisciplinary and interrelated field. Samples of these fresh trends are presented in this volume, based on contributions from the Workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2013. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists and researchers in the field of Lie Theory.
Geometry.
Mathematical physics.
Topological groups.
Lie groups.
Geometry.
Mathematical Physics.
Topological Groups, Lie Groups.