  We revisit the Schrieffer-Wolff transformation and present a path integral
version of this important canonical transformation. The equivalence between the
low-energy sector of the Anderson model in the so-called local moment regime
and the spin-isotropic Kondo model is usually established via a canonical
transformation performed on the Hamiltonian, followed by a projection. Here we
present a path integral formulation of the Schrieffer-Wolff transformation
which relates the functional integral form of the partition function of the
Anderson model to that of its effective low-energy model. The resulting
functional integral assumes the form of a spin path integral and includes a
geometric phase factor, i.e. a Berry phase. Our approach stresses the
underlying symmetries of the model and allows for a straightforward
generalization of the transformation to more involved models. It thus not only
sheds new light on a classic problem, it also offers a systematic route of
obtaining effective low-energy models and higher order corrections.
