Instanton-like excitations in 2D fermionic field theory

Abstract

In this article we review some recent results previously reported in [1,2], where a new type of nonperturbative excitations was identified in the Thirring and Schwinger models.This effect is explicitly observed in the light-cone quantization using functional methods.The effect arises from the need to compactify the x − coordinate in the light-cone, which in effect changes the spacetime topology.Integrating out the right-handed fermions (ψ R ) yields an effective action for left-handed fermions (ψ L ) which contains excitations similar to abelian instantons produced by a composite of ψ L . Right-handed fermions don't have a similar effective action and therefore, quantum mechanically, the symmetry ψ L ↔ ψ R must be broken as a result of the topology. The conserved charge associated to the topological states is quantized. Different cases *