Covariance of noncommutative Grassmann star product

Abstract

Using the Coherent states of many fermionic degrees of freedom labeled by Graßmann variables, we introduce the noncommutative (precisely non anticommutative) Graßmann star product. The covariance of star product under unitary transformations, particularly canonical ones, is studied. The super star product, based on supercoherent states of supersymmetric harmonic oscillator, is also considered.