We investigate finite volume effects in the pattern of chiral symmetry breaking. To this end we employ a formulation of the Schwinger-Dyson equations on a torus which reproduces results from the corresponding lattice simulations of staggered quarks and from the overlap action. Studying the volume dependence of the quark propagator we find quantitative differences with the infinite volume result at small momenta and small quark masses. We estimate the minimal box length $L$ below which chiral perturbation theory cannot be applied to be $L\simeq 1.6\mathrm{fm}$. In the infinite volume limit we find a chiral condensate of $|⟨\overline{q}q⟩{|}_{\overline{MS}}^{2\mathrm{GeV}}=(253\pm 5\mathrm{MeV}{)}^3$, an up/down quark mass of $m_{\overline{MS}}^{2\mathrm{GeV}}=4.1\pm 0.3\mathrm{MeV}$ and a pion decay constant which is only 10% smaller than the experimental value.

• Received 20 December 2005

DOI:https://doi.org/10.1103/PhysRevD.73.034029