Chiral invariant Gross-Neveu model: Classical versus quantum

We present a unification of different and independently investigated aspects of the chiral invariant Gross-Neveu model. Special emphasis is placed on the relevance of classical (c-number, non Grassmann) spinor solutions of the G-N field equations for the construction, and thus understanding of the respective quantized Fermi model. To get an insight into the “quantum meaning of classical field theory” if specialized to the G-N case, we perform the path integral quantization procedure which first leads to the Fermi oscillator problem, and then, after appropriate generalizations, to the quantum Fermi G-N model. Path integrals are carried out with respect to c-number spinor paths only, and in fact no reference is necessary to the Grassmann algebra methods, which are conventionally used to integrate out fermions.