DIFFEOMORPHISM GROUPS AND CURRENT ALGEBRAS: CONFIGURATION SPACE ANALYSIS IN QUANTUM THEORY

Author:

ALBEVERIO S.1,KONDRATIEV YU. G.23,RÖCKNER M.4

Affiliation:

1. Fakultät für Mathematik, Ruhr-Universität, D 44780 Bochum, Germany

2. Forschungszentrum BiBoS, Bielefeld Universität, D 33615 Bielefeld, Germany

3. Institute of Mathematics, Nasu, 252601 Kiev, Ukraine

4. Fakultät für Mathematik, Bielefeld Universität, D 33615 Bielefeld, Germany

Abstract

The constuction of models of non-relativistic quantum fields via current algebra representations is presented using a natural differential geometry of the configuration space Γ of particles, the corresponding classical Dirichlet operator associated with a Poisson measure on Γ, being the free Hamiltonian. The case with interactions is also discussed together with its relation to the problem of unitary representations of the diffeomorphism group on ℝd.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

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