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

R. Coquereaux (auth.), C. Bartocci, U. Bruzzo, R. Cianci (eds.)3540537635, 9783540537632, 0387537635

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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Table of contents :
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 Kähler manifolds….Pages 155-161
A new class of infinite-dimensional Lie algebras (continuum Lie algebras) and associated nonlinear systems….Pages 162-170
Exchange Algebra in the Conformal Affine sl 2 Toda Field Theory….Pages 173-184
Some properties of p-lines….Pages 185-197
Breaking of supersymmetry through anomalies in composite spinor operators….Pages 198-208
Conformal field theory and moduli spaces of vector bundles over variable Riemann surfaces….Pages 209-218
Instanton homology….Pages 219-221
W- geometry….Pages 222-244
Connections between CFT and topology via Knot theory….Pages 245-254
Stochastic calculus in superspace and supersymmetric Hamiltonians….Pages 255-262
Geometric models and the modulli spaces for string theories….Pages 263-268
Supersymmetric products of SUSY-curves °….Pages 271-285
Classical superspaces and related structures….Pages 286-297
Remarks on the differential identities in Schouten-Nijenhuis algebra….Pages 298-310
Generic irreducible representations of classical Lie superalgebras….Pages 311-319
Krichever construction of solutions to the super KP hierarchies….Pages 320-330
The structure of supersymplectic supermanifolds….Pages 331-343
Gauge fixing: Geometric and probabilistic aspects of yang-mills gauge theories….Pages 347-358
A renormalizable theory of quantum gravity….Pages 359-371
Third order nonlinear Hamiltonian systems: Some remarks on the the action-angle transformation….Pages 375-378
Tensor products of q p = 1 quantum groups and WZW fusion rules….Pages 379-381
The modular group and super-KMS functionals….Pages 382-384
New quantum representation for gravity and Yang-Mills theory….Pages 385-386
Geometric quantization of the five-dimensional Kepler problem….Pages 387-389
Structure functions on the usual and exotic symplectic and periplectic supermanifolds….Pages 390-395
Symbols alias generating functionals — a supergeometric point of view….Pages 396-398
Sheaves of graded Lie algebras over variable Riemann surfaces and a paired Weil-Petersson inner product….Pages 399-401