Ebook: Differential Geometric Methods in Theoretical Physics: Proceedings of the 19th International Conference Held in Rapallo, Italy 19–24 June 1990

Geometry, if understood properly, is still the closest link between mathematics and theoretical physics, even for quantum concepts. In this collection of outstanding survey articles the concept of non-commutation geometry and the idea of quantum groups are discussed from various points of view. Furthermore the reader will find contributions to conformal field theory and to superalgebras and supermanifolds. The book addresses both physicists and mathematicians.

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Geometry, if understood properly, is still the closest link between mathematics and theoretical physics, even for quantum concepts. In this collection of outstanding survey articles the concept of non-commutation geometry and the idea of quantum groups are discussed from various points of view. Furthermore the reader will find contributions to conformal field theory and to superalgebras and supermanifolds. The book addresses both physicists and mathematicians.
Content:
Front Matter....Pages -
Higgs fields and superconnections....Pages 3-12
Noncommutative differential geometry, quantum mechanics and gauge theory....Pages 13-24
Introduction to non-commutative geometry and Yang-Mills model-building....Pages 25-36
II. Gauge-field model-building via non-commutative differential geometry....Pages 37-44
Measuring coalgebras, quantum group-like objects, and non-commutative geometry....Pages 47-60
Tensor Operator Structures in Quantum Unitary Groups....Pages 61-69
Quantum groups and quantum complete integrability: Theory and experiment....Pages 71-90
Some ideas and results on integrable nonlinear evolution systems....Pages 91-95
An algebraic characterization of complete integrability for Hamiltonian systems....Pages 96-106
Integrable lattice models and their scaling limits QFT and CFT....Pages 107-119
Quantum groups, Riemann surfaces and conformal field theory....Pages 120-130
Some physical applications of category theory....Pages 131-142
From poisson groupoids to quantum groupoids and back....Pages 143-154
Quantization on K?hler manifolds....Pages 155-161
A new class of infinite-dimensional Lie algebras (continuum Lie algebras) and associated nonlinear systems....Pages 162-170
Some properties of p-lines....Pages 173-184
Breaking of supersymmetry through anomalies in composite spinor operators....Pages 185-197
Conformal field theory and moduli spaces of vector bundles over variable Riemann surfaces....Pages 198-208
Instanton homology....Pages 209-218
W- geometry....Pages 219-221
Connections between CFT and topology via Knot theory....Pages 222-244
Stochastic calculus in superspace and supersymmetric Hamiltonians....Pages 245-254
Geometric models and the modulli spaces for string theories....Pages 255-262
Supersymmetric products of SUSY-curves °....Pages 263-268
Classical superspaces and related structures....Pages 271-285
Remarks on the differential identities in Schouten-Nijenhuis algebra....Pages 286-297
Generic irreducible representations of classical Lie superalgebras....Pages 298-310
Krichever construction of solutions to the super KP hierarchies....Pages 311-319
The structure of supersymplectic supermanifolds....Pages 320-330
Gauge fixing: Geometric and probabilistic aspects of yang-mills gauge theories....Pages 331-343
A renormalizable theory of quantum gravity....Pages 347-358
Third order nonlinear Hamiltonian systems: Some remarks on the the action-angle transformation....Pages 359-371
The modular group and super-KMS functionals....Pages 375-378
New quantum representation for gravity and Yang-Mills theory....Pages 379-381
Geometric quantization of the five-dimensional Kepler problem....Pages 382-384
Structure functions on the usual and exotic symplectic and periplectic supermanifolds....Pages 385-386
Symbols alias generating functionals — a supergeometric point of view....Pages 387-389
Sheaves of graded Lie algebras over variable Riemann surfaces and a paired Weil-Petersson inner product....Pages 390-395
....Pages 396-398