Balachandran A.P., Bimonte G., Landi G.,, Lizzi F. Teotonio-Sobrinho P.
Lattice Gauge Fields and Noncommutative Geometry
(92K, LaTeX, 33 pages)
ABSTRACT. Conventional approaches to lattice gauge theories do not properly
consider the topology of spacetime or of its fields. In this paper, we
develop a formulation which tries to remedy this defect. It starts
from a cubical decomposition of the supporting manifold (compactified
spacetime or spatial slice) interpreting it as a finite topological
approximation in the sense of Sorkin. This finite space is entirely
described by the algebra of cochains with the cup product. The methods
of Connes and Lott are then used to develop gauge theories on this
algebra and to derive Wilson's actions for the gauge and Dirac fields
therefrom which can now be given geometrical meaning. We also describe
very natural candidates for the QCD $\theta $-term and Chern-Simons
action suggested by this algebraic formulation. Some of these
formulations are simpler than currently available alternatives. The
paper treats both the functional integral and Hamiltonian approaches.
Report-no: ESI(1995)299, SU-4240-621, DFTUZ/96/06, DSF-T-15/96, UICHEP-TH/95-12