BRST Symmetry and the Scale Transformation of Ghost Fields in Gauge Theory on NC Spacetime

Abstract

BRST symmetry is very important to quantize gauge theory and to construct a covariant canonical formulation. It may also be important for gauge theory on noncommutative (NC) spacetime. The BRST symmetry of U(N) gauge theory on NC spacetime has recently been studied by Soroush, who manipulated the component fields of the gauge and fermion fields. We define the BRST transformations of the representation fields of gauge and fermion fields and show its nilpotency in a transparent way. The scale symmetry of ghost fields is also investigated. BRST charge and FP ghost charge are derived and shown to be the generators of the respective symmetries. As a byproduct, it is shown that Noether’s theorem is recovered on NC spacetime by redefining the current.