The classical mechanics for bose-fermi systems

• DOI: 10.1007/bf02729860
• Publication Date: 2007-12-18T13:37:59Z
• Authors: R. Casalbuoni
• Keywords: 0103 physical sciences; 01 natural sciences

In this paper we study in a systematic way the classical mechanics of systems described byc-number variables and by Grassmann variables. We derive the general form of the nonrelativistic action and we study the theory of canonical transformations. For a general action, we show that the Jacobian matrices of the canonical transformations acting onN Grassmann variables form a groupO N, N . This group becomesO N for the nonrelativistic action, due to the presence of second-class constraints. We study some examples which give rise to a correct classical description of the spin. Considering a relativistic extension of one of these models, we get a first quantized «substratum» for the superfield theories.