Classical limit of fermions in phase space

Abstract

Using the mathematical structure of the Grassmann algebra, studied by Schönberg, we write down the Pauli equation and the Dirac equation in phase space. In addition, in order to investigate the physical nature of the spin degree of freedom inherent in these equations we set up a novel classical limiting process ℏ→0. Thus we are able to derive relativistic and nonrelativistic classical statistical mechanics, for particle with spin 1/2, within a geometric algebra framework. © 2001 American Institute of Physics.