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

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

1995-12-29

arxiv.org/abs/hep-th/9512215v1

J.Math.Phys.37:3725-3738,1996

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTeX file

Scientific paper

10.1063/1.531598

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.

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