A generalization of the Bargmann-Fock representation to supersymmetry

In the Bargmann-Fock representation the coordinates zi act as bosonic reation operators while the partial derivatives δzs act as annihilation operators on holomorphic 0-forms as states of a D-dimensional bosonic oscillator. Also considering p-forms and further geometrical objects as the exterior derivative and Lie derivatives on a holomorphic CD, we end p with an analogous representation for the D-dimensional supersymmetric oscillator. In particular, the supersymmetry multiplet structure of the Hilbert space corresponds to the cohomology of the exterior derivative. In addition, a 1-complex parameter group emerges naturally and contains both time evolution and a homotopy related to cohomology. The emphasis is on calculus. (author)