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Geometric Methods in Physics

XXXI Workshop, Białowieża, Poland, June 24–30, 2012

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Piotr Kielanowski

    1. Departamento de Física, CINVESTAV, Mexico City, Mexico

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  2. S. Twareque Ali

    1. Dept. of Mathematics and Statistics, Concordia University, Montreal, Canada

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  3. Alexander Odesskii

    1. Department of Mathematics - MC J415, Brock University, St. Catharines, Canada

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  4. Anatol Odzijewicz

    1. Institute of Mathematics, University of Bialystok, Bialystok, Poland

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  5. Martin Schlichenmaier

    1. Mathematics Research Unit, FSTC, University of Luxembourg, Luxembourg-Kirchberg, Luxembourg

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  6. Theodore Voronov

    1. School of Mathematics, University of Manchester, Manchester, United Kingdom

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  • Provides an overview of the recent state of the interaction of geometry with modern physics
  • Discusses the work and important contributions of Boris Fedosov to deformation quantization
  • Contains contributions of leading scientists in the field
  • Discusses physical topics in a mathematically precise way

Part of the book series: Trends in Mathematics (TM)

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About this book

The Białowieża workshops on Geometric Methods in Physics, taking place in the unique environment of the Białowieża natural forest in Poland, are among the important meetings in the field. Every year some 80 to 100 participants both from mathematics and physics join to discuss new developments and to interchange ideas. The current volume was produced on the occasion of the XXXI meeting in 2012. For the first time the workshop was followed by a School on Geometry and Physics, which consisted of advanced lectures for graduate students and young researchers. Selected speakers of the workshop were asked to contribute, and additional review articles were added. The selection shows that despite its now long tradition the workshop remains always at the cutting edge of ongoing research. The XXXI workshop had as a special topic the works of the late Boris Vasilievich Fedosov (1938–2011) who is best known for a simple and very natural construction of a deformation quantization for any symplectic manifold, and for his contributions to index theory.​

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Table of contents (22 papers)

  1. Front Matter

    Pages i-x
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  2. Quantization, the Scientific Legacy of B.V. Fedosov

    1. Front Matter

      Pages 1-2
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    2. Non-formal Deformation Quantization and Star-exponential of the Poincaré Group

      • Pierre Bieliavsky, Axel de Goursac, Florian Spinnler
      Pages 3-12

    3. Spinc, Mpc and Symplectic Dirac Operators

      • Michel Cahen, Simone Gutt
      Pages 13-28

    4. \(\theta(\hat{x},\hat{p})\)-deformation of the Harmonic Oscillator in a 2D-phase Space

      • M. N. Hounkonnou, D. Ousmane Samary, E. Baloïtcha, S. Arjika
      Pages 29-37

    5. Star Products and Certain Star Product Functions

      • Mari Iida, Chishu Tsukamoto, Akira Yoshioka
      Pages 39-45

    6. Paragrassmann Algebras as Quantum Spaces Part I: Reproducing Kernels

      • Stephen Bruce Sontz
      Pages 47-63

  3. Groups, Algebras and Symmetries

    1. Front Matter

      Pages 65-65
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    2. Rolling of Coxeter Polyhedra Along Mirrors

      • Dmitri V. Alekseevski, Peter W. Michor, Yurii A. Neretin
      Pages 67-86

    3. Boundedness for Pseudo-differential Calculus on Nilpotent Lie Groups

      • Ingrid Beltiţă, Daniel Beltiţă, Mihai Pascu
      Pages 87-97

    4. A Useful Parametrization of Siegel–Jacobi Manifolds

      • Stefan Berceanu
      Pages 99-108

    5. An Application of the Reduction Method to Sutherland type Many-body Systems

      • L. Fehér
      Pages 109-117

    6. Lagrange Anchor for Bargmann–Wigner Equations

      • D. S. Kaparulin, S. L. Lyakhovich, A. A. Sharapov
      Pages 119-126

    7. The Laplace Transform, Mirror Symmetry, and the Topological Recursion of Eynard–Orantin

      • Motohico Mulase
      Pages 127-142

    8. An Elementary Proof of the Formal Rigidity of the Witt and Virasoro Algebra

      • Martin Schlichenmaier
      Pages 143-153

    9. Invariants for Darboux Transformations of Arbitrary Order for \(\mathcal{D}_x\mathcal{D}_y+a\mathcal{D}_x+b\mathcal{D}_y+c\)

      • Ekaterina Shemyakova
      Pages 155-162

    10. Decomposition of Weyl Group Orbit Products of W(A2)

      • Agnieszka Tereszkiewicz
      Pages 163-168

  4. General Methods

    1. Front Matter

      Pages 169-169
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    2. On Operators Generated by Maps with Separable Dynamics

      • A. Antonevich, A. Akhmatova
      Pages 171-178

    3. From the Heat Equation to Ordinary Differential Equations

      • Elena Yu. Bunkova
      Pages 179-185
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Editors and Affiliations

  • Departamento de Física, CINVESTAV, Mexico City, Mexico

    Piotr Kielanowski

  • Dept. of Mathematics and Statistics, Concordia University, Montreal, Canada

    S. Twareque Ali

  • Department of Mathematics - MC J415, Brock University, St. Catharines, Canada

    Alexander Odesskii

  • Institute of Mathematics, University of Bialystok, Bialystok, Poland

    Anatol Odzijewicz

  • Mathematics Research Unit, FSTC, University of Luxembourg, Luxembourg-Kirchberg, Luxembourg

    Martin Schlichenmaier

  • School of Mathematics, University of Manchester, Manchester, United Kingdom

    Theodore Voronov

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