Heidelberg 1999 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 1: Hauptvortr
äge I

MP 1.3: Invited Talk

Monday, March 15, 1999, 15:40–16:30, MA1

Quantum mechanics as a gauge theory on phase-space — •Martin Reuter — Institut für Theoretische Physik, Universität Mainz

Quantum mechanics is reformulated in terms of a universal Yang-Mills theory over phase-space. It involves an infinite-dimensional gauge group, a nondynamical connection, and metaplectic spinors as “matter fields” providing a local generalization of states and observables. They assume values in a family of local Hilbert spaces (and their tensor products) which are attached to the points of phase-space. Under local frame rotations they transform in the spinor representation of the metaplectic group Mp(2N), the double covering of Sp(2N). The rules of canonical quantization are replaced by two new postulates with a more transparent physical meaning and with a simple group theoretical and differential geometrical interpretation.

Lit.: M.Reuter, Int.J.Mod.Phys. A13 (1998) 3835