On the Correct Convergence of Complex Langevin Simulations for Polynomial Actions

There are problems in physics and particularly in field theory which are defined by complex valued weight functions $e^{-S}$ where $S$ is a polynomial action $S: R^n \rightarrow C$. The conditions under which a convergent complex Langevin calculation correctly simulates such integrals are discussed. All conditions on the process which are used to prove proper convergence are defined in the stationary limit.