Complex actions for fermions in higher dimensions

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Abstract
We discuss the generalization of the complex Langevin approach to fermionic path integrals for more than d=1+1 dimensions. Whereas one found convincing results in d≤1+1 there are difficulties with the convergence properties of the complex processes even for free relativistic fermions for d=2+1. Satisfactory results are obtained only for very small lattices or in a certain asymmetric limit of the coupling parameters.