Differential Geometrical Methods in Theoretical Physics

Front Matter....Pages i-xvii
The Impact of Physics on Geometry....Pages 1-9
Weyl’s Program and Modern Physics....Pages 11-36
Elliptic Genera of Level N for Complex Manifolds....Pages 37-63
The Principle of Triality and A Distinguished Unitary Representation of SO(4,4)....Pages 65-108
On E 10 ....Pages 109-128
Operator Methods in String Theory....Pages 129-144
On Strings and J.Douglas Variational Principle....Pages 145-148
Groupoids and Lie Bigebras in Gauge and String Theories....Pages 149-164
The Definition of Conformal Field Theory....Pages 165-171
Statistics and Monodromy in Two- and Three-Dimensional Quantum · Field Theory....Pages 173-186
Quantum Groups (YBZF Algebras) and Integrable Theories: An Overview....Pages 187-210
Integrable Systems and Conformal Invariance....Pages 211-218
Algebraic Aspects of Non-Perturbative Quantum Field Theories....Pages 219-259
The pairing method and bosonic anomalies....Pages 261-293
A Multisymplectic Approach to the KdV Equation....Pages 295-305
Singular Points in Level Sets of the Momentum Map and Quantum Theory....Pages 307-315
Killing Spinors and Universality of the Hijazi Inequality....Pages 317-332
Towards a Renormalizable Theory of Quantum Gravity....Pages 333-343
Gauge Theory for Diffeomorphism Groups....Pages 345-371
Quantum Field Theory in Curved Spacetime....Pages 373-393
Supertheories....Pages 395-404
The Integrability Of N = 16 Supergravity....Pages 405-405
Conformal Invariant Supersymmetric Theories in Four Dimensions: A Practical Application of BRS Cohomology....Pages 407-415
Supermanifolds, Supermanifold Cohomology, and Super Vector Bundles....Pages 417-440
Representations of Lie Superalgebras an Introduction....Pages 441-460
Concluding Remarks....Pages 461-461
Observations of Two of Our Brightest Stars....Pages 463-471