The Cartan Model for Equivariant Cohomology

In this article, we will discuss a new operator $d_C$ on $W(\mathfrak{g})\otimes {\mathrm{\Omega }}^{\ast }(M)$ and to construct a new Cartan model for equivariant cohomology. We use the new Cartan model to construct the corresponding BRST model and Weil model, and discuss the relations between them.