BRST model for equivariant cohomology and representatives for the equivariant thom class

In this paper the BRST formalism for topological field theories is studied in a mathematical setting. The BRST operator is obtained as a member of a one parameter family of operators connecting the Weil model and the Cartan model for equivariant cohomology. Furthermore, the BRST operator is identified as the sum of an equivariant derivation and its Fourier transform. Using this, the Mathai-Quillen representative for the Thom class of associated vector bundles is obtained as the Fourier transform of a simple BRST closed element.Supported by the SV FOM/SMC Mathematical Physics, The Netherlands