  The quantization of the massless Thirring model in the light-cone using
functional methods is considered. The need to compactify the coordinate $x^-$
in the light-cone spacetime implies that the quantum effective action for
left-handed fermions contains excitations similar to abelian instantons
produced by composite of left-handed fermions. Right-handed fermions don't have
a similar effective action. Thus, quantum mechanically, chiral symmetry must be
broken as a result of the topological excitations. The conserved charge
associated to the topological states is quantized. Different cases with only
fermionic excitations or bosonic excitations or both can occur depending on the
boundary conditions and the value of the coupling.
