Geometric Methods in Physics

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

      PDF

   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

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.​

• Boris Fedosov
• coherent states
• geometry
• mathematical physics
• quantum states
• superspaces

• 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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