Differential Geometrical Methods in Mathematical Physics

Proceedings of the Symposium Held at the University at the University of Bonn, July 1 - 4, 1975
1. Auflage 1977
ISBN: 978-3-540-08068-8
Verlag: Springer

Buch, Englisch, Französisch, Band 570, 582 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1810 g

Reihe: Lecture Notes in Mathematics

Springer Book Archives

Zielgruppe

Research

Autoren/Hrsg.

Bleuler, K.

Reetz, A.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

An outline of geometric quantisation (d'après Kostant).- The metalinear geometry of non-real polarizations.- On cohomology groups appearing in geometric quantization.- Geometric quantization and Feynman path integrals for spin.- V. Fock, 40 years later.- Interpretation geometrique des etats quantiques.- Geometric structure of quantization.- The application of graded Lie algebras to invariance considerations in particle physics.- Some recent results on supersymmetry.- Graded manifolds, graded Lie theory, and prequantization.- Gauge fields as quantized connection forms.- Complex line bundles and the magnetic field of a monopole.- Conclusions from an extended gauge principle of Dirac's equation.- Reducibility of the symplectic structure of classical fields with gauge-symmetry.- New geometrical dynamics.- On the generalization of symplectic geometry to multiple integrals in the Calculus of Variations.- A symplectic formulation of particle dynamics.- A symplectic formulation of field dynamics.- Canonical transformations and their representations in quantum mechanics.- On a symplectic structure of general relativity.- On the symplectic formulation of the einstein system of evolution in presence of a self-gravitating scalar field.- Invertible foliations and type D-spaces.- Deformations of the embedded Einstein spaces.- The causal structure of singularities.- Towards quantum gravity.- Remarks about Dirac's idea of cosmological variation of so called ‘constants of nature’.