Topological fluctuations and breaking of chiral symmetry in gauge theories involving massless fermions

Using the method of Euclidean functional integrals, we show the occurrence of a certain types of chiral symmetry breaking as a result of local fluctuations in the winding number. We mainly restrict our discussion to QED₂ in order to have an independent check of our methods from the known solution of this model. We do not use instantons (pseudo-particles), and we also avoid functional integration over fields with global winding (Pontryagin) number different from zero.