Lie Theory and Its Applications in Physics, 1st Edition

  • Published By:
  • ISBN-10: 4431542701
  • ISBN-13: 9784431542704
  • DDC: 512.55
  • Grade Level Range: College Freshman - College Senior
  • 554 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation 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. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantum groups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples of these new 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 2011. This book is suitable for an extensive audience of mathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theory.

Table of Contents

Front Cover.
Editorial Board.
Other Frontmatter.
Title Page.
Copyright Page.
List of Participants.
1: Plenary Talks.
2: A Lump Solution in SFT.
3: Towards p-Adic Matter in the Universe.
4: Palev Statistics and the Chronon.
5: Some Remarks on Weierstrass Sections, Adapted Pairs and Polynomiality.
6: From Palev's Study of Wigner Quantum Systems to New Results on Sums of Schur Functions.
7: Varna Lecture on L2-Analysis of Minimal Representations.
8: Exponential Series Without Denominators.
9: New Methods in Conformal Partial Wave Analysis.
10: Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly.
11: Wigner Quantization and Lie Superalgebra Representations.
12: Quantum Field Theory.
13: Spontaneous Breaking of Supersymmetry, Localization and Nicolai Mapping in Matrix Models.
14: Mirror Map as Generating Function of Intersection Numbers.
15: Operadic Construction of the Renormalization Group.
16: String and Gravity Theories.
17: Lightlike Braneworlds in Anti-de Sitter Bulk Space-Times.
18: Generalized Bernoulli Polynomials and the Casimir Effect in the Einstein Universe.
19: From Singularities to Algebras to Pure Yang-Mills with Matter.
20: On Modified Gravity.
21: Quantum Groups and Related Objects.
22: The q-Wakimoto Realization of the Superalgebras Uq(sl̂(N|1))) and Uq,p(sl(N|1))).
23: Quantum Phases in Noncommutative Space.
24: On Quantum WZNW Monodromy Matrix: Factorization, Diagonalization, and Determinant.
25: Representation Theory.
26: Some Properties of Planar Galilean Conformal Algebras.
27: Invariant Differential Operators for Non-compact Lie Groups: The Sp(n, IR) Case.
28: Generalization of the Gell-Mann Decontraction Formula for sl(n, ℝ) and Its Applications in Affine Gravity.
29: W-Algebras Extending gl(1|1).
30: Non-Local Space-Time Transformations Generated from the Ageing Algebra.
31: Construction of the Noncommutative Rank I Bergman Domain.
32: Vertex Algebras.
33: Singular Vectors and Zhu's Poisson Algebra of Parafermion Vertex Operator Algebras.
34: Boson-Fermion Correspondence of Type B and Twisted Vertex Algebras.
35: On Twisted Modules for N=2 Supersymmetric Vertex Operator Superalgebras.
36: Integrability and Other Applications.
37: The Ruijsenaars Self-Duality Map as a Mapping Class Symplectomorphism.
38: Hilbert Space Decomposition for Coulomb Blockade in Fabry-Pérot Interferometers.
39: Group Classification of Variable Coefficient KdV-like Equations.
40: A New Diffeomorphism Symmetry Group of Magnetohydrodynamics.
41: Invariance Properties of the Exceptional Quantum Mechanics (F4) and Its Generalization to Complex Jordan Algebras (E6).
42: Matrix Superpotentials.
43: Various Mathematical Results.
44: On Finite W-Algebras for Lie Superalgebras in the Regular Case.
45: Young Tableaux and Homotopy Commutative Algebras.
46: Fixed Point Factorization.
47: Differential Invariants of Second-Order Ordinary Differential Equations.
48: Some Properties of Harmonic Quasi-Conformal Mappings.
49: A Note on the Categorification of Lie Algebras.
50: A Continuous Bialgebra Structure on a Loop Algebra.