Geometric Methods in Physics, 1st Edition

  • Published By:
  • ISBN-10: 3034806450
  • ISBN-13: 9783034806459
  • DDC: 530.15
  • Grade Level Range: College Freshman - College Senior
  • 237 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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.​

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
A Word About Boris Vasil′evich Fedosov.
1: Quantization, the Scientific Legacy of B.V. Fedosov.
2: Non-formal Deformation Quantization and Star-exponential of the Poincaré Group.
3: Spinc, Mpc and Symplectic Dirac Operators.
4: θ(x, p-deformation of the Harmonic Oscillator in a 2D-phase Space.
5: Star Products and Certain Star Product Functions.
6: Paragrassmann Algebras as Quantum Spaces Part I: Reproducing Kernels.
7: Groups, Algebras and Symmetries.
8: Rolling of Coxeter Polyhedra Along Mirrors.
9: Boundedness for Pseudo-differential Calculus on Nilpotent Lie Groups.
10: A Useful Parametrization of Siegel-Jacobi Manifolds.
11: An Application of the Reduction Method to Sutherland type Many-body Systems.
12: Lagrange Anchor for Bargmann-Wigner Equations.
13: The Laplace Transform, Mirror Symmetry, and the Topological Recursion of Eynard–Orantin.
14: An Elementary Proof of the Formal Rigidity of the Witt and Virasoro Algebra.
15: Invariants for Darboux Transformations of Arbitrary Order for DxDy + aDx + bDy + c.
16: Decomposition of Weyl Group Orbit Products of W(A2).
17: General Methods.
18: On Operators Generated by Maps with Separable Dynamics.
19: From the Heat Equation to Ordinary Differential Equations.
20: 4-planar Mappings of Quaternionic Kähler Manifolds.
21: Unduloid-like Equilibrium Shapes of Carbon Nanotubes Subjected to Hydrostatic Pressure.
22: Resonance Phenomenon for Potentials of Wigner-von Neumann Type.
23: Form Factor Approach to the Calculation of Correlation Functions of Integrable Models.
24: On Space-like Hypersurfaces in a Space-time.
25: On Bogomolny Decompositions for the Baby Skyrme Models.