Differential Geometry, Group Representations, and Quantization

E. Binz (auth.), Jö-Dieter Hennig, Wolfgang Lücke, Jiří Tolar (eds.)3540539417, 9783540539414, 0387539417

Differential geometry and analytic group theory are among the most powerful tools in mathematical physics. This volume presents review articles on a wide variety of applications of these techniques in classical continuum physics, gauge theories, quantization procedures, and the foundations of quantum theory. The articles, written by leading scientists, address both researchers and grad- uate students in mathematics, physics, and philosophy of science.

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Table of contents :
Global differential geometric methods in elasticity and hydrodynamics….Pages 1-29
GL( n , ℝ), tetrads and generalized space-time dynamics….Pages 31-42
On boundary conditions for Yang-Mills fields in spatially bounded domains….Pages 43-53
Parallel transport of phases….Pages 55-72
An alternative approach to the quantization of linear relativistic field equations….Pages 75-83
A lattice approximation of the dirac equation….Pages 85-97
Some hidden aspects of hidden symmetry….Pages 99-108
A baryon standard model for electroweak and strong interactions….Pages 109-136
Is the physical vacuum really Lorentz-invariant?….Pages 137-143
Quantization, coherent states and diffeomorphism groups….Pages 145-178
Borel quantization and the origin of topological effects in quantum mechanics….Pages 179-190
Symmetries of quantum group coupling coefficients….Pages 191-206
Symmetry groups and spectrum generating groups….Pages 207-226
Spectrum and character formulae of so(3, 2) unitary representations….Pages 227-238
Quantum theory of single events….Pages 239-256
Symmetry, entropy and complexity….Pages 257-264
Steps in the philosophy of quantum theory….Pages 265-280