A note on Gaussian integrals over paragrassmann variables

Details A note on Gaussian integrals over paragrassmann variables A note on Gaussian integrals over paragrassmann variables

2002-09-20

arxiv.org/abs/hep-th/0209172v1

Int.J.Mod.Phys. A19 (2004) 1705-1714

Physics

High Energy Physics

High Energy Physics - Theory

12 pages

Scientific paper

10.1142/S0217751X04018506

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.

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