Supersymmetric Classical Mechanics

Abstract

In the present chapter we consider the classical version of the supersymmetric Witten model. Actually, these kinds of supersynmietric classical systems can be considered as special cases of so-called pseudoclassical models. The notion of pseudoclassical mechanics has been introduced in 1976 by Casalbuoni [Cas76b] and describes classical systems which in addition to their usual bosonic (commuting) also have fermionic (anticommuting) degrees of freedom. In fact, pseudoclassical systems can be xmderstood as the classical limit of quantum systems which have both kinds of degree of freedom [Cas76b]. Pseudoclassical mechanics is of particular interest because of its ability to describe spin-degrees of freedom on a classical level [BeMa75, Cas76a, BaCaLu76, BrDeZuVeHo76, BeMa77, BaBoCa81, LaDoGu93]. For an alternative classical spin model see [BaZa84, Bar86].