Differential Geometrical Methods in Mathematical Physics II -

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Résumé :
On the role of field theories in our physical conception of geometry.- Characteristic classes and solutions of gauge theories.- Classification of classical yang-mills fields.- Bundle representations and their applications.- to gauge theory.- The use of exterior forms in field theory.- Electromagnetic fields on manifolds: Betti numbers, monopoles and strings, minimal coupling.- Gravity is the gauge theory of the parallel - transport modification of the poincare group.- On the lifting of structure groups.- On the non-uniqueness of spin structure in superconductivity.- Conformal invariance in field theory.- Geometric quantization and the WKB approximation.- Some properties of half-forms.- On some approach to geometric quantization.- Representations associated to minimal co-adjoint orrits.- On the Schr?dinger equation given by geometric quantisation.- Application of geometric quantization in quantum mechanics.- Thermodynamique et Geometrie.- Some preliminary remarks on the formal variational calculus of gel'fand and dikii.- Reducibility of the symplectic structure of minimal interactions.- Ambiguities in canonical transformations of classical systems and the spectra of quantum observables.- Quantum field theory in curved space-times a general mathematical framework.- On functional integrals in curved spacetime.- Observables for quantum fields on curved background.- Quantization of fields on a curved background.- Supergravity.- Representations of classical lie superalgebras....

Sommaire:
On the role of field theories in our physical conception of geometry.- Characteristic classes and solutions of gauge theories.- Classification of classical yang-mills fields.- Bundle representations and their applications.- to gauge theory.- The use of exterior forms in field theory.- Electromagnetic fields on manifolds: Betti numbers, monopoles and strings, minimal coupling.- Gravity is the gauge theory of the parallel - transport modification of the poincare group.- On the lifting of structure groups.- On the non-uniqueness of spin structure in superconductivity.- Conformal invariance in field theory.- Geometric quantization and the WKB approximation.- Some properties of half-forms.- On some approach to geometric quantization.- Representations associated to minimal co-adjoint orrits.- On the Schr?dinger equation given by geometric quantisation.- Application of geometric quantization in quantum mechanics.- Thermodynamique et Geometrie.- Some preliminary remarks on the formal variational calculus of gel'fand and dikii.- Reducibility of the symplectic structure of minimal interactions.- Ambiguities in canonical transformations of classical systems and the spectra of quantum observables.- Quantum field theory in curved space-times a general mathematical framework.- On functional integrals in curved spacetime.- Observables for quantum fields on curved background.- Quantization of fields on a curved background.- Supergravity.- Representations of classical lie superalgebras.