A note on Gaussian integrals over paragrassmann variables

LETICIA F CUGLIANDOLO; GUSTAVO S LOZANO; ENRIQUE MORENO; FIDEL A SCHAPOSNIK

INTERNATIONAL JOURNAL OF MODERN PHYSICS A

Año: 2004 vol. A p. 1705 - 1714

0217-751X

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 [$\theta^{p+1}=0$ 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 q-deformed 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.