arXiv subjects

A. Dimakis

Publications and source records attributed to A. Dimakis.

20 records · Page 2Linked to original sources

arXiv1994

Noncommutative Differential Calculus: Quantum Groups, Stochastic Processes, and the Antibracket

We explore a differential calculus on the algebra of smooth functions on a manifold. The former is `noncommutative' in the sense that functions and differentials do not commute, in general. Relations with bicovariant differential calculus on certain quantum groups and stochastic calculus are discussed. A similar differential calculus on a superspace is shown to be related to the Batalin-Vilkovisky antifield formalism.

hep-th↗

arXiv1994

Differential calculus and gauge theory on finite sets

We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (which is an essential ingredient of his reformulation of the standard model of elementary particle physics) is recovered in our approach. Reductions of the universal differential calculus to `lower-dimensional' differential calculi are considered. The `complete reduction' leads to a differential calculus on a periodic lattice which is related to q-calculus.

hep-th↗