Path integrals with generalized Grassmann variables

Abstract

We construct path integral representations for the evolution operator of q-oscillators with root of unity values of the q-parameter using Bargmann-Fock representations with commuting and noncommuting variables, the differential calculi being q-deformed in both cases. For q 2 = −1, i.e. for the case of usual anticommuting (fermionic) variables, we obtain a new form of the Grassmann-like path integral.