Lie Theory and Its Applications in Physics

1. Front Matter

   Pages i-xv

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2. Plenary Talks

   1. Front Matter

      Pages 1-1

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   2. \(*\)–Lie Algebras Canonically Associated to Probability Measures on \({\pmb {\varvec{\mathbb {R}}}}\) with All Moments

      • Luigi Accardi, Abdessatar Barhoumi, Yun Gang Lu, Mohamed Rhaima

      Pages 3-21

   3. Special Conformal Transformations and Contact Terms

      • Loriano Bonora

      Pages 23-34

   4. On Nonlocal Modified Gravity and Its Cosmological Solutions

      • Ivan Dimitrijevic, Branko Dragovich, Jelena Stankovic, Alexey S. Koshelev, Zoran Rakic

      Pages 35-51

   5. Kinetics of Interface Growth: Physical Ageing and Dynamical Symmetries

      • Malte Henkel

      Pages 53-65

   6. News on SU(2|1) Supersymmetric Mechanics

      • Evgeny Ivanov, Stepan Sidorov

      Pages 67-81

   7. Intrinsic Sound of Anti-de Sitter Manifolds

      • Toshiyuki Kobayashi

      Pages 83-99

   8. Sphere Partition Functions and the Kähler Metric on the Conformal Manifold

      • Efrat Gerchkovitz, Zohar Komargodski

      Pages 101-110

   9. Real Group Orbits on Flag Ind-Varieties of \(\mathrm {SL}(\infty ,\mathbb {C})\)

      • Mikhail V. Ignatyev, Ivan Penkov, Joseph A. Wolf

      Pages 111-135

   10. Derived Functors and Intertwining Operators for Principal Series Representations of \(SL_2({\pmb {\mathbb {R}}})\)

       • Raul Gomez, Birgit Speh

       Pages 137-150

   11. Hyperlogarithms and Periods in Feynman Amplitudes

       • Ivan Todorov

       Pages 151-167

   12. The Parastatistics Fock Space and Explicit Infinite-Dimensional Representations of the Lie Superalgebra \({\mathfrak {osp}}(2m+1|2n)\)

       • N. I. Stoilova, J. Van der Jeugt

       Pages 169-180

   13. Stepwise Square Integrable Representations: The Concept and Some Consequences

       • Joseph A. Wolf

       Pages 181-202

   14. Higher-Dimensional Unified Theories with Continuous and Fuzzy Coset Spaces as Extra Dimensions

       • G. Manolakos, G. Zoupanos

       Pages 203-229

3. String Theories and Gravity Theories

   1. Front Matter

      Pages 231-231

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   2. Higher Genus Amplitudes in SUSY Double-Well Matrix Model for 2D IIA Superstring

      • Fumihiko Sugino

      Pages 233-243

   3. Kruskal–Penrose Formalism for Lightlike Thin-Shell Wormholes

      • Eduardo Guendelman, Emil Nissimov, Svetlana Pacheva, Michail Stoilov

      Pages 245-259

   4. Metric-Independent Spacetime Volume-Forms and Dark Energy/Dark Matter Unification

      • Eduardo Guendelman, Emil Nissimov, Svetlana Pacheva

      Pages 261-273

   5. Large Volume Supersymmetry Breaking Without Decompactification Problem

      • Hervé Partouche

      Pages 275-284

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.
Recently, the trend has been 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 employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.

• 17BXX, 20-XX, 22-XX, 43-XX, 16GXX, 16TXX, 81TXX
• Proceedings
• Representation Theory
• Infinite-Dimensional Lie Groups and Algebras
• Functional Analysis
• Integrable Systems
• Algebraic Geometry
• Number Theory
• Quantum Groups
• Superalgebras and Supergroups
• Symmetries in String Theory
• Supergravity
• Conformal Field Theories
• Nonrelativistic Theories

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

  Vladimir Dobrev

Policies and ethics