This volumes provides a comprehensive review of interactions between differential geometry and theoretical physics, contributed by many leading scholars in these fields. The contributions promise to play an important role in promoting the developments in these exciting areas. Besides the plenary talks, the coverage includes: models and related topics in statistical physics; quantum fields, strings and M-theory; Yang-Mills fields, knot theory and related topics; K-theory, including index theory and non-commutative geometry; mirror symmetry, conformal and topological quantum field theory; development of integrable systems; and random matrix theory"
Author(s): Zhang M. L. (Ed)
Year: 2006
Language: English
Pages: 542
CONTENTS ......Page 14
Foreword by Michael Atiyah ......Page 8
Foreword by Chen Ning Yang ......Page 10
Preface ......Page 12
Plenary Lectures ......Page 20
Yangian and Applications ......Page 22
The hypoelliptic Laplacian and Chern-Gauss-Bonnet......Page 57
S. S. Chern and Chern-Simons Terms ......Page 72
Localization and Conjectures from String Duality ......Page 82
Topologization of Electron Liquids with Chern-Simons Theory and Quantum Computation ......Page 125
Invited Contributions ......Page 140
Quasicrystals: Projections of 5-d Lattice into 2 and 3 Dimensions ......Page 142
Theoretical Analysis of the Double Spin Chain Compound KCuCl3......Page 152
Applications of Geometric Cluster Algorithms ......Page 161
Equivariant Cohomology and Localization for Lie Algebroids and Applications ......Page 171
Directed Percolation in Two Dimensions: An Exact Solution ......Page 179
Generalized Drinfeld Polynomials for Highest Weight Vectors of the Borel Subalgebra of the sl2 Loop Algebra......Page 188
On the Physical Significance of q-deformation in Many-body Physics......Page 198
A Matrix Product Ansatz Solution of an Exactly Solvable Interacting Vertex Model ......Page 209
A 2h-dimensional Model with Virasoro Symmetry ......Page 219
3-dimensional Integrable Lattice Models and the Bazhanov- Stroganov Model ......Page 229
Exact Solution of Two Planar Polygon Models ......Page 240
Quasi-exact Solvability of Dirac Equations ......Page 251
Exotic Galilean Symmetry, Non-commutativity & the Hall Effect
......Page 260
The Energy-momentum and Related Topics in Gravitational Radiation ......Page 267
Quantum Operators and Hermitian Vector Fields ......Page 275
Electric-magnetic Duality Beyond Four Dimensions and in General Relativity ......Page 285
Topology and Quantum Information ......Page 292
Generalized Cohomologies and Differential Forms of Higher Order ......Page 302
Periodic Cellular Automata and Bethe Ansatz ......Page 312
An L²-Alexander-Conway Invariant for Knots and the Volume Conjecture......Page 322
Faddeev Knots, Skyrme Solitons, and Concentration-Compactness......Page 332
Dynamics of Bose-Einstein Condensates ......Page 342
Twisted Space-Time Symmetry, Non-Commutativity and Particle Dynamics......Page 352
Toeplitz Quantization and Symplectic Reduction ......Page 362
On Mysteriously Missing T-duals, H-flux and the T-duality Group......Page 369
Murphy Operators in Knot Theory ......Page 378
Bethe Ansatz for the Open XXZ Chain from Functional Relations at Roots of Unity ......Page 386
Separation Between Spin And Charge in SU(2) Yang-Mills Theory ......Page 396
On Solutions of the One-dimensional Holstein Model ......Page 403
Recent Developments on Ising and Chiral Potts Model ......Page 408
Bethe Ansatz and Symmetry in Superintegrable Chiral Potts Model and Root-of-unity Six-vertex Model ......Page 418
The Cyclic Renormalization Group ......Page 429
Bohm-Aharonov Type Effects in Dissipative Atomic Systems ......Page 439
Noncommutative Procedures in Spontaneous Symmetry Breaking and Quantum Differentiation ......Page 448
Löwner Equations and Dispersionless Hierarchies......Page 457
Multiparameter Quantum Deformations of Jordanian Type for Lie Superalgebras ......Page 462
A Correlation-Function Bell Inequality with Improved Visibility for 3 Qubits ......Page 472
Topological Aspects of the Spin Hall Effect ......Page 481
Positive Mass Theorems and Calabi-Yau Compactification ......Page 492
Analytic Torsion and an Invariant of Calabi-Yau Threefold ......Page 499
Differential Galois Groups of High Order Fuchsian ODE's......Page 509
Conformal Triality of de Sitter, Minkowski and Anti-de Sitter
Spaces......Page 522
Some Observations on Gopakumar-Vafa Invariants of Some Local Calabi-Yau Geometries ......Page 532
