BRS Symmetry in Connes' Non-commutative Geometry

Abstract

We extend the BRS and anti-BRS symmetry to the two point space of Connes' non-commutative model building scheme. The constraint relations are derived and the quantum Lagrangian constructed. We find that the quantum Lagrangian can be written as a functional of the curvature for symmetric gauges with the BRS, anti-BRS auxiliary field finding a geometrical interepretation as the extension of the Higgs scalar.