A generalization of the Bargmann  Fock representation to supersymmetry
Abstract
In the Bargmann  Fock representation the coordinates 03054470/29/21/028/img1 act as bosonic creation operators while the partial derivatives 03054470/29/21/028/img2 act as annihilation operators on holomorphic 0forms as states of a Ddimensional bosonic oscillator. Also considering pforms and further geometrical objects as the exterior derivative and Lie derivatives on a holomorphic 03054470/29/21/028/img3, we end up with an analogous representation for the Ddimensional supersymmetric oscillator. In particular, the supersymmetry multiplet structure of the Hilbert space corresponds to the cohomology of the exterior derivative. In addition, a 1complex parameter group emerges naturally and contains both time evolution and a homotopy related to cohomology. The emphasis is on calculus.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 1996
 DOI:
 10.1088/03054470/29/21/028
 arXiv:
 arXiv:hepth/9511155
 Bibcode:
 1996JPhA...29.6983T
 Keywords:

 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 11 pages, LaTeX