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Lie Theory and Its Applications in Physics

Varna, Bulgaria, June 2013

  • Conference proceedings
  • © 2014

Overview

Editors:
  1. Vladimir Dobrev

    1. Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria

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  • Presents new advances in Lie theory and its applications in physics
  • Contains articles from top researchers in the field
  • Covers many different applications and stimulates further research in the area

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 111)

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About this book

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.

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Table of contents (44 papers)

  1. Front Matter

    Pages i-xiii
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  2. Plenary Talks

    1. Front Matter

      Pages 1-1
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    2. Revisiting Trace Anomalies in Chiral Theories

      • Loriano Bonora, Stefano Giaccari, Bruno Lima De Souza
      Pages 3-12

    3. Complete T-Dualization of a String in a Weakly Curved Background

      • Lj. Davidović, B. Nikolić, B. Sazdović
      Pages 13-20

    4. Modular Double of the Quantum Group \(SL_{q}(2, \mathbb{R})\)

      • L. D. Faddeev
      Pages 21-31

    5. Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance

      • Malte Henkel, Stoimen Stoimenov
      Pages 33-50

    6. New Type of \(\mathcal{N} = 4\) Supersymmetric Mechanics

      • Evgeny Ivanov, Stepan Sidorov
      Pages 51-66

    7. Vector-Valued Covariant Differential Operators for the Möbius Transformation

      • Toshiyuki Kobayashi, Toshihisa Kubo, Michael Pevzner
      Pages 67-85

    8. Semi-classical Scalar Products in the Generalised SU(2) Model

      • Ivan Kostov
      Pages 87-103

    9. Weak Poisson Structures on Infinite Dimensional Manifolds and Hamiltonian Actions

      • K.-H. Neeb, H. Sahlmann, T. Thiemann
      Pages 105-135

    10. Bethe Vectors of gl(3)-Invariant Integrable Models, Their Scalar Products and Form Factors

      • Eric Ragoucy
      Pages 137-154

    11. Polylogarithms and Multizeta Values in Massless Feynman Amplitudes

      • Ivan Todorov
      Pages 155-176

    12. Reduction of Couplings in Quantum Field Theories with Applications in Finite Theories and the MSSM

      • S. Heinemeyer, M. Mondragón, N. Tracas, G. Zoupanos
      Pages 177-196

  3. String Theories and Gravity Theories

    1. Front Matter

      Pages 197-197
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    2. A SUSY Double-Well Matrix Model as 2D Type IIA Superstring

      • Fumihiko Sugino
      Pages 199-209

    3. f(R)-Gravity: “Einstein Frame” Lagrangian Formulation, Non-standard Black Holes and QCD-Like Confinement/Deconfinement

      • E. Guendelman, A. Kaganovich, E. Nissimov, S. Pacheva
      Pages 211-221

    4. The D-Brane Charges of C 3/\(\mathbb{Z}_{2}\)

      • Elaine Beltaos
      Pages 223-230

    5. On Robertson Walker Solutions in Noncommutative Gauge Gravity

      • Simona Babeti
      Pages 231-239

    6. Some Power-Law Cosmological Solutions in Nonlocal Modified Gravity

      • Ivan Dimitrijevic, Branko Dragovich, Jelena Grujic, Zoran Rakic
      Pages 241-250

    7. On Nonlocal Modified Gravity and Cosmology

      • Branko Dragovich
      Pages 251-262
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Editors and Affiliations

  • Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria

    Vladimir Dobrev

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