Differential Geometry, Group Representations, and Quantization

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. Global Differential Geometric Methods In Elasticity And Hydrodynamics / E. Binz -- Gl(n, Ir) Tetrads And Generalized Space-time Dynamics / J.j. Slawianowski -- On Boundary Conditions For Yang-mills Fields In Spatially Bounded Domains / J. Śniatycki -- Parallel Transport Of Phases / A. Uhlmann -- An Alternative Approach To The Quantization Of Linear Relativistic Field Equations / G.c. Hegerfeldt -- A Lattice Approximation Of The Dirac Equation / J. Kijowski And A. Thielmann -- Some Hidden Aspects Of Hidden Symmetry / L. O'raifeartaigh -- A Baryonstandard Model For Electroweak And Strong Interactions / R. Ra̧czka -- Is The Physical Vacuum Really Lorentz-invariant? / I.e. Segal -- Quantization, Coherent States And Diffeomorphism Groups / S.t. Ali And G.a. Goldin -- Borel Quantization And The Origin Of Topological Effects In Quantum Mechanics / J. Tolar. Symmetries Of Quantum Group Coupling Coefficients / L.c. Biedenharn And M.a. Lohe -- Symmetry Groups And Spectrum Generating Groups / A. Bohm -- Spectrum And Character Formulae Of So(3,2) Unitary Representations / V.k. Dobrev And E. Sezgin -- Quantum Theory Of Single Events / A.o. Barut -- Symmetry, Entropy And Complexity / Y. Ne'eman -- Steps In The Philosophy Of Quantum Theory / Th. Görnitz And C.f. Weizsäcker. J.d. Hennig, W. Lücke, J. Tolar (eds.) Includes Bibliographical References. 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 This volume presents a series of review articles on the applications of differential geometry and analytic group theory in classical continuum physics, gauge theories, quantization procedures and the foundations of quantum theory.