Geometric Methods in Physics: Proceedings of the XXVIII Workshop on Geometric Methods in Physics: Bialowieza, Poland, 28 June-4 July 2009

by Kielanowski, Piotr; Ali, S. Twareque; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore

• ISBN13: 9780735407282
• ISBN10: 0735407282
• Format: Hardcover
• Copyright: 2009-12-31
• Publisher: Amer Inst of Physics

Summary

The conference was devoted to a wide range of mathematical problems related to description of quantum and/or classical physical systems. From the point of view of physics the main attention was paid to such topics as quantization of classical systems, path integrals, rigid bodies and graded algebras. Mathematical aspects of these topics occupy the following branches: Poisson and symplectic geometry, Lie algebras, C*-algebras, spectral theory, non-commutative geometry, Riemannian spaces, differential equations, cryptography and some others.

Table of Contents

Preface	p. vii
Participants	p. ix
Group Photograph	p. xi
On Extensions of the Legendre Transform	p. 1
A Survey on Weyl Calculus for Representations of Nilpotent Lie Groups	p. 7
The Jacobi Group and the Squeezed States—Some Comments	p. 21
Non-Formal Deformation Quantization and Symmetric Spaces	p. 30
Heat Equations and Sigma Functions	p. 46
Global Anomaly and Stability of Fold Product of Complex Two-Cycles	p. 59
Path Space Forms and Surface Holonomy	p. 66
Rigid Body Systems of Hess-Appel'rot Type and Partial Reductions	p. 72
Relativistic Equations for Spin Particles: What can We Learn from Noncommutativity?	p. 80
The Poisson Equations in the Nonholonomic Suslov Problem: Integrabillty, Meromorphic and Hypergeometric Solutions	p. 85
Some Integrable Systems on the Banach Lie-Poisson Space iR?u1 res	p. 91
¿(Ric)-Vector Fields on Conformally Flat Spaces	p. 98
An Algebraic Method of Factorization of Ordinary Differential Operators	p. 104
Discretization of Tori of Exceptional Compact Simple Lie Groups	p. 110
Quantum Ball	p. 116
A Poisson Structure in White-Noise Analysis	p. 123
On the Analyticity of the Bergman Transform	p. 127
On the Whewell Parameterization of the Euler Elastica	p. 133
Graded Commutative Algebras: Examples, Classification, Open Problems	p. 141
Quasicrystal Models in Cryptography	p. 148
Invariant Variational Problems and Cartan Connections on Gauge-Natural Bundles	p. 160
Spectra of Photon Down Conversion	p. 166
Geometry and Dynamics of the Pentagram Map	p. 172
Group Transformations with Discrete Parameter and Invariant Schrödinger Equation	p. 182
Examples of Star Exponentials	p. 188
Author Index	p. 195
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