A quantization condition due to the boundary conditions and the
compatification of the light cone space-time coordinate x− is identified at
the level of the classical equations for the right-handed fermionic field in
two dimensions. A detailed analysis of the implications of the implementation
of this quantization condition at the quantum level is presented. In the case
of the Thirring model one has selection rules on the excitations as a function
of the coupling and in the case of the Schwinger model a double integer
structure of the vacuum is derived in the light-cone frame. Two different
quantized chiral Schwinger models are found, one of them without a
θ-vacuum structure. A generalization of the quantization condition to
theories with several fermionic fields and to higher dimensions is presented.Comment: revtex, 14 p