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- W2069650934 abstract "We study the Hamilton formalism for Connes-Lott models, i.e., for Yang-Mills theory in non-commutative geometry. The starting point is an associative $*$-algebra $cA$ which is of the form $cA=C(I,cAs)$ where $cAs$ is itself a associative $*$-algebra. With an appropriate choice of a k-cycle over $cA$ it is possible to identify the time-like part of the generalized differential algebra constructed out of $cA$. We define the non-commutative analogue of integration on space-like surfaces via the Dixmier trace restricted to the representation of the space-like part $cAs$ of the algebra. Due to this restriction it possible to define the Lagrange function resp. Hamilton function also for Minkowskian space-time. We identify the phase-space and give a definition of the Poisson bracket for Yang-Mills theory in non-commutative geometry. This general formalism is applied to a model on a two-point space and to a model on Minkowski space-time $times$ two-point space." @default.
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- W2069650934 date "1996-04-01" @default.
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- W2069650934 title "Hamilton formalism in non-cummutative geometry" @default.
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