Point canonical transformations in the path integral formulation of supersymmetric quantum mechanics

Abstract

We investigate the question of general covariance of the continuous path integral representation for supersymmetric quantum mechanics. First we show that a quadratic point canonical transformation does not affect the perturbation expansion at the two-loop level, where anomalies could appear. Then we show in general that the perturbation expansion is covariant analyzing the discrete rigorous definition of the path integral representation and prove that the mid-point definition is covariant. The results obtained correspond to those previously established in the operator formalism.