A note on Gaussian integrals over paragrassmann variables

We discuss the generalization of the connection between the determinant of an operator entering a quadratic form and the associated Gaussian path-integral valid for grassmann variables to the paragrassmann case [θp+1 = 0 with p = 1 (p > 1) for grassmann (paragrassamann) variables]. We show that the q-deformed commutation relations of the paragrassmann variables lead naturally to consider qdeformed quadratic forms related to multiparametric deformations of GL(n) and their corresponding q-determinants. We suggest a possible application to the study of disordered systems. Conicet Associated with CICPBA 1 Using anticommuting functions as integration variables, Matthews and Salam showed that the path-integral for a system of relativistic fermions in an external field gives the determinant of the Dirac operator [1]. That is, the fermionic partition function does not yield a negative power of the determinant, as in the bosonic case, but a positive power, p = +1. Ten years later, Berezin completed his analysis of noncommutative algebras and fermion systems, making clear that the natural framework to define fermionic path-integrals was that of Grassmann algebras [2]. The main ingredient behind the result