Infinite Dimensional Groups and ManifoldsTilman Wurzbacher The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics. Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern-Weil construction in infinite dimensions, the hamiltonian approach to quantum field theory, and different aspects of large N limits ranging from approximation methods in quantum mechanics to modular forms and string/gauge theory duality. The volume gives an overview of important themes of research at the forefront of mathematics and theoretical physics. |
Contents
Lie groups of germs of analytic mappings | 1 |
The flow completion of the Burgers equation | 17 |
Enumerative geometry and knot invariants | 27 |
Gerbes twisted Ktheory and the supersymmetricWZW model | 93 |
Current groups for noncompact manifolds and their central extensions | 108 |
Traces and characteristic classes on loop spaces | 184 |
New classical limits of quantum theories | 213 |
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Common terms and phrases
asymptotic Banach boundary Calabi-Yau Calabi-Yau manifold central extension Chern classes Chern-Simons theory classical closed coefficients compact manifold compact subset complex analytic conifold connected component convex direct limit corresponding D-branes defined denote diffeomorphism differential dimension direct limit discrete dR,c equation example field theory finite finite-dimensional follows Fréchet free energy gauge group geometry gerbe given Gromov-Witten invariants H₁ H₁(X hamiltonian Hecke operators hence holomorphic homotopy equivalence implies infinite dimensional instantons int(X integral isomorphism K-analytic K-theory knot Lemma Lie algebra Lie group linear map locally convex direct locally convex space loop groups Math modular forms obtain open string Phys polynomial Proof quantum representation Riemann surface smooth function smooth maps string theory subgroup subspace Theorem topological strings torus trace trivial trº Vafa vanish vector field vevs Wilson loops