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.
In this topical volume, invited experts survey applications of differential geometry and group theory in classical and quantum physics. They address both researchers and students.
Global differential geometric methods in elasticity and hydrodynamics.- GL(n, ?), tetrads and generalized space-time dynamics.- On boundary conditions for Yang-Mills fields in spatially bounded domains.- Parallel transport of phases.- An alternative approach to the quantization of linear relativistic field equations.- A lattice approximation of the dirac equation.- Some hidden aspects of hidden symmetry.- A baryon standard model for electroweak and strong interactions.- Is the physical vacuum really Lorentz-invariant?.- Quantization, coherent states and diffeomorphism groups.- Borel quantization and the origin of topological effects in quantum mechanics.- Symmetries of quantum group coupling coefficients.- Symmetry groups and spectrum generating groups.- Spectrum and character formulae of so(3, 2) unitary representations.- Quantum theory of single events.- Symmetry, entropy and complexity.- Steps in the philosophy of quantum theory.