Quantum deformation of classical Grassmann algebras

Abstract

Following a treatment analogous to that of Wess and Zumino, we quantize the classical Grassmann algebras by developing a differential calculus on then-dimensional quantum hyperplane spanned by the generators of a nonanticommutative algebra. We show that the calculus so developed is covariant under the action of the quantum groupGLq(n) satisfying all the general constraints. In the limiting case of a real quantum plane, this calculus can be considered as a deformation of the quantum-mechancial phase space of a Fermi system.