Compactness of the solution operator to d-bar in weighted L² - spaces

In this paper we discuss compactness of the canonical solution operator to d-bar on weigthed L^2- spaces on C^n. For this purpose we apply ideas which were used for the Witten Laplacian in the real case and various methods of spectral theory of these operators. We also point out connections to the theory of Dirac and Pauli operators.