BRST Quantization of Gauge Theory in Noncommutative Geometry: Matrix Derivative Approach

The BRST quantization of a gauge theory in noncommutative geometry is carried out in the “matrix derivative” approach. BRST/anti-BRST transformation rules are obtained by applying the horizontality condition, in the superconnection formalism. A BRST/anti-BRST invariant quantum action is then constructed, using an adaptation of the method devised by Baulieu and Thierry-Mieg for the Yang-Mills case. The resulting quantum action turns out to be the same as that of a gauge theory in the ’t Hooft gauge with spontaneously broken symmetry. Our result shows that only the even part of the supergroup acts as a gauge symmetry, while the odd part effectively provides a global symmetry. We treat the general formalism first, then work out the SU(2/1) and SU(2/2) cases explicitly. PACS number(s): 02.40.-k, 12.10.-g, 12.15.Cc # Also on leave from: Center for Particle Physics, University of Texas, Austin, Tx 78712, USA