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MP: Theoretische und Mathematische Grundlagen der Physik

MP 1: Klassische Feldtheorie, Nichtkommutative Geometrie

MP 1.2: Fachvortrag

Monday, March 24, 2003, 15:30–16:00, F309

Time evolutions in Quantum mechanics and (Lorentzian) geometry — •Mario Paschke — Matematicky ustav, Bezrucovo namesti 13, 74601 Opava, Czech republik

As R.Feynman has shown to F. Dyson – who published it then in 1990 under the name of No-dqFeynman’s proof of Maxwell’s equationsNo-dq – the only interactions compatible with the canonical uncertainty relation (for scalar particles on flat euclidean space) are the elctromagnetic interactions.

We generalize Feynman’s argument to arbitrary configuration spaces, thereby clarifying its hidden assumptions as well as its geometrical significance. At the same time, we obtain an algebraic formulation of quantum mechanics, which can be applied to many systems with noncommutative configuration spaces as well.

As an immediate consequence our result also establishes a correspondence between solutions to our axioms and globally hyperbolic spacetimes.