Differential geometrical methods in mathematical physics

Configuration spaces of identical particles....Pages 1-8
The geometrical meaning and globalization of the Hamilton-Jacobi method....Pages 9-21
The Euler-Lagrange resolution....Pages 22-48
On the prequantum description of spinning particles in an external gauge field....Pages 49-66
Classical action, the wu-yang phase factor and prequantization....Pages 67-90
Groupes differentiels....Pages 91-128
Representations that remain irreducible on parabolic subgroups....Pages 129-144
Non-positive polarizations and half-forms....Pages 145-152
Connections on symplectic manifolds and geometric quantization....Pages 153-166
Geometric aspects of the feynman integral....Pages 167-170
Relativistic quantum theory in complex spacetime....Pages 171-176
Existence et equivalence de deformations associatives associees a une variete symplectique....Pages 177-185
A new symplectic structure of field theory....Pages 186-201
Conformal structures and connections....Pages 202-210
Equilibrium configurations of fluids in general relativity....Pages 211-220
Quaternionic and supersymmetric σ — models....Pages 221-245
Supergravity as the gauge theory of supersymmetry....Pages 246-255
Hypergravities....Pages 256-262
Preface....Pages 265-265
Preface....Pages 266-268
Morse theory and the yang-mills equations....Pages 269-275
Reduction of the yang mills equations....Pages 276-291
Tangent structure of Yang-Mills equations and hodge theory....Pages 292-312
Classification of gauge fields and group representations....Pages 313-317
Gauge asthenodynamics (SU(2/1)) (classical discussion)....Pages 318-348
Spinors on fibre bundles and their use in invariant models....Pages 349-358
Glueing broken symmetries together....Pages 359-365
Deformations and quantization....Pages 366-374
Stability theory and quantization....Pages 375-382
Presymplectic manifolds and the quantization of relativistic particle systems....Pages 383-400
Geometric quantisation for singular lagrangians....Pages 401-405
Electron scattering on magnetic monopoles....Pages 406-419
The metaplectic representation, weyl operators and spectral theory....Pages 420-431
Supergravity: A unique self-interacting theory....Pages 432-439
General relativity as a gauge theory....Pages 440-454
On a purely affine formulation of general relativity....Pages 455-461
A fibre bundle description of coupled gravitational and gauge fields....Pages 462-483
Homogenous symplectic formulation of field dynamics and the poincaré-cartan form....Pages 484-497
Spectral sequences and the inverse problem of the calculus of variations....Pages 498-503
Geodesic fields in the calculus of variations of multiple integrals depending on derivatives of higher order....Pages 504-511
Separability structures on riemannian manifolds....Pages 512-538