Why the Thirring model cannot fulfill canonical anticommutation relations

Perturbative and constructive arguments show that the Gross-Neveu model with N greater than or equal to 2 flavor degrees is asymptotically free. Assuming canonical anticommutation relations (CAR), which are quite plausible, and some technicalities, we show for the Thirring model, i.e., the case of N = 1 flavor, that the fields are necessarily free. This explains from an axiomatic point of view the different behavior depending on the number of flavors. (C) 1996 American Institute of Physics.