  We consider the quark-meson-model in a finite three-dimensional volume using
the Schwinger proper-time renormalization group. We derive and solve the flow
equations for finite volume in local potential approximation. In order to break
chiral symmetry in the finite volume, we introduce a small current quark mass.
The corresponding effective meson potential breaks chiral O(4) symmetry
explicitly, depending on sigma and pion fields separately. We calculate the
volume dependence of the pion mass and of the pion decay constant with the
renormalization group flow equations and compare with recent results from
chiral perturbation theory in a finite volume.
