The classical mechanics for Bose-Fermi systems

The classical mechanics of systems described by c-number variables and by Grassmann variables are studied in a systematic way. The general form of the nonrelativistic action and the theory of canonical transformations are considered. For a general action, the Jacobian matrices of the canonical transformations acting on N Grassmann variables form a group O/sub N, N/. This group becomes O/sub N/ for the nonrelativistic action, due to the presence of second class constraints. Some examples which give rise to a correct classical description of the spin are studied. Considering a relativistic extension of one of these models, a first quantized 'substratum' for the superfield theories is determined. (22 refs).