池森 均

We introduce the basic equivariant quantity $Q$ in the gauge theory on the<br /> noncommutative descrete $Z_{2}$ space, which plays an important role for the<br /> equivariant dimensional reduction. If the gauge configuration of the ground<br /> state on the extra dimensional space is described by the equivariant $Q$, then<br /> the extra dimensional space is invisible. Especially, using the equivariance<br /> principle, we show that the Yang-Mills theory on $R^{2}\times Z_{2}$ space is<br /> equivalent to the Yang-Mills-Higgs model on $R^{2}$ space. It can be said that<br /> this model is the simplest model of this type.

The Batalin-Vilkovisky antifield action for the BF theories is constructed by<br /> means of the extended form method. The BRST invariant BV antifield action is<br /> directly written down by making use of the extended forms that involve all the<br /> required ghosts and antifields.