Franklin

Differential Geometric Methods in Theoretical Physics [electronic resource] : Proceedings of the 19th International Conference Held in Rapallo, Italy, 19–24 June 1990 / edited by CLAUDIO BARTOCCI, Ugo Bruzzo, Roberto Cianci.

Publication:
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991.
Format/Description:
Book
1 online resource (XIX, 404 p. 4 illus.)
Edition:
1st ed. 1991.
Series:
Lecture Notes in Physics, 0075-8450 ; 375
Lecture Notes in Physics, 0075-8450 ; 375
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Subjects:
Mathematical physics.
Differential geometry.
Local subjects:
Theoretical, Mathematical and Computational Physics. (search)
Differential Geometry. (search)
Language:
English
Summary:
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.
Contents:
Higgs fields and superconnections
Noncommutative differential geometry, quantum mechanics and gauge theory
to non-commutative geometry and Yang-Mills model-building
II. Gauge-field model-building via non-commutative differential geometry
Measuring coalgebras, quantum group-like objects, and non-commutative geometry
Tensor Operator Structures in Quantum Unitary Groups
Quantum groups and quantum complete integrability: Theory and experiment
Some ideas and results on integrable nonlinear evolution systems
An algebraic characterization of complete integrability for Hamiltonian systems
Integrable lattice models and their scaling limits QFT and CFT
Quantum groups, Riemann surfaces and conformal field theory
Some physical applications of category theory
From poisson groupoids to quantum groupoids and back
Quantization on Kähler manifolds
A new class of infinite-dimensional Lie algebras (continuum Lie algebras) and associated nonlinear systems
Exchange Algebra in the Conformal Affine sl 2 Toda Field Theory
Some properties of p-lines
Breaking of supersymmetry through anomalies in composite spinor operators
Conformal field theory and moduli spaces of vector bundles over variable Riemann surfaces
Instanton homology
W- geometry
Connections between CFT and topology via Knot theory
Stochastic calculus in superspace and supersymmetric Hamiltonians
Geometric models and the modulli spaces for string theories
Supersymmetric products of SUSY-curves °
Classical superspaces and related structures
Remarks on the differential identities in Schouten-Nijenhuis algebra
Generic irreducible representations of classical Lie superalgebras
Krichever construction of solutions to the super KP hierarchies
The structure of supersymplectic supermanifolds
Gauge fixing: Geometric and probabilistic aspects of yang-mills gauge theories
A renormalizable theory of quantum gravity
Third order nonlinear Hamiltonian systems: Some remarks on the the action-angle transformation
Tensor products of q p = 1 quantum groups and WZW fusion rules
The modular group and super-KMS functionals
New quantum representation for gravity and Yang-Mills theory
Geometric quantization of the five-dimensional Kepler problem
Structure functions on the usual and exotic symplectic and periplectic supermanifolds
Symbols alias generating functionals — a supergeometric point of view
Sheaves of graded Lie algebras over variable Riemann surfaces and a paired Weil-Petersson inner product.
Notes:
Bibliographic Level Mode of Issuance: Monograph
Contributor:
BARTOCCI, CLAUDIO. editor., Editor,
Bruzzo, Ugo. editor., Editor,
Cianci, Roberto. editor., Editor,
ISBN:
3-540-47090-5
Publisher Number:
10.1007/3-540-53763-5 doi