Noncommutative Geometry -- Poisson Geometry and Deformation Quantization -- Applications in Physics -- Topological Quantum Field Theory.This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challeng…
Knot Invariants and Configuration Space Integrals (Christine Lescop) -- Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces (Raimar Wulkenhaar) -- Introduction to String Compactification (Anamaria Font, Stefan Theisen) -- Index Theorems and Noncommutative Topology (Thierry Fack).This volume offers an introduction, in the form of four extensive lectures, to some recent develo…
Introduction -- The Ernst Equation -- Riemann-Hilbert Problem and Fay's Identity -- Analyticity Properties and Limiting Cases -- Boundary Value Problems and Solutions -- Hyperelliptic Theta Functions and Spectral Methods -- Physical Properties -- Open Problems -- Riemann Surfaces and Theta Functions -- Ernst Equation and Twister Theory -- Index.Exact solutions to Einstein`s equations have been …
1 Relativity based on symmetry -- 1.1 Space-time transformation based on relativity -- 1.2 Step 6 - Identification of invariants -- 1.3 Relativistic velocity addition -- 1.4 Step 7 - The velocity ball as a bounded symmetric domain -- 1.5 Step 8 - Relativistic dynamics -- 1.6 Notes -- 2 The real spin domain -- 2.1 Symmetric velocity addition -- 2.2 Projective and conformal commutativity and asso…