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We propose new techniques for the numerical implementation of theoverlap-Dirac operator, which exploit the physical properties of the underlyingtheory to avoid nested algorithms. We test these procedures in thetwo-dimensional Schwinger model and the results are very promising. Thesetechniques can be directly applied to QCD simulations. We also present adetailed computation of the spectrum and the chiral properties of the Schwingermodel in the overlap lattice formulation.Comment: minor corrections, to appear on Phys. Rev.

Schwinger model with the overlap-Dirac operator: Exact results versus a physics motivated approximation