HAMILTON FORMALISM IN NONCOMMUTATIVE GEOMETRY

We study the Hamilton formalism for Connes-Lott models, i.e. for Yang- Mills theory in noncommutative geometry. The starting point is an asso ciative -algebra A which is of the form A = C(I, A(s)), where A(s) is itself an associative -algebra. With an appropriate choice of a K-cy cle over A it is possible to identify the time-like part of the genera lized differential algebra constructed out of A. We define the non-com mutative analogue of integration on space-like surfaces via the Dixmie r trace restricted to the representation of the space-like part A(s) o f the algebra. Due to this restriction it is possible to define the La grange function resp. Hamilton function also for Minkowskian spacetime . We identify the phase-space and give a definition of the Poisson bra cket for Yang-Mills theory in non-commutative geometry. This general f ormalism is applied to a model on a two-point space and to a model on Minkowski space-time x two-point space.