Lattice Gauge Fields and Noncommutative Geometry

Details Lattice Gauge Fields and Noncommutative Geometry Lattice Gauge Fields and Noncommutative Geometry

1996-04-15

arxiv.org/abs/hep-lat/9604012v2

J.Geom.Phys. 24 (1998) 353-385

Physics

High Energy Physics

High Energy Physics - Lattice

34 pages, Latex, Minor corrections, Section 6 corrected

Scientific paper

10.1016/S0393-0440(97)00017-X

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.

Affiliated with

Also associated with

No associations

Rating

Lattice Gauge Fields and Noncommutative Geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lattice Gauge Fields and Noncommutative Geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lattice Gauge Fields and Noncommutative Geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-215938