Differential Geometrical Methods in Mathematical Physics

Inhaltsverzeichnis

• Configuration spaces of identical particles.
• The geometrical meaning and globalization of the Hamilton-Jacobi method.
• The Euler-Lagrange resolution.
• On the prequantum description of spinning particles in an external gauge field.
• Classical action, the wu-yang phase factor and prequantization.
• Groupes differentiels.
• Representations that remain irreducible on parabolic subgroups.
• Non-positive polarizations and half-forms.
• Connections on symplectic manifolds and geometric quantization.
• Geometric aspects of the feynman integral.
• Relativistic quantum theory in complex spacetime.
• Existence et equivalence de deformations associatives associees a une variete symplectique.
• A new symplectic structure of field theory.
• Conformal structures and connections.
• Equilibrium configurations of fluids in general relativity.
• Quaternionic and supersymmetric ? — models.
• Supergravity as the gauge theory of supersymmetry.
• Hypergravities.
• Preface.
• Morse theory and the yang-mills equations.
• Reduction of the yang mills equations.
• Tangent structure of Yang-Mills equations and hodge theory.
• Classification of gauge fields and group representations.
• Gauge asthenodynamics (SU(2/1)) (classical discussion).
• Spinors on fibre bundles and their use in invariant models.
• Glueing broken symmetries together.
• Deformations and quantization.
• Stability theory and quantization.
• Presymplectic manifolds and the quantization of relativistic particle systems.
• Geometric quantisation for singular lagrangians.
• Electron scattering on magnetic monopoles.
• The metaplectic representation, weyl operators and spectral theory.
• Supergravity: A unique self-interacting theory.
• General relativity as a gauge theory.
• On a purely affine formulation of general relativity.
• A fibre bundledescription of coupled gravitational and gauge fields.
• Homogenous symplectic formulation of field dynamics and the poincaré-cartan form.
• Spectral sequences and the inverse problem of the calculus of variations.
• Geodesic fields in the calculus of variations of multiple integrals depending on derivatives of higher order.
• Separability structures on riemannian manifolds.