SUPERSYMMETRY AND NONCOMMUTATIVE GEOMETRY

The purpose of this article is to apply the concept of the spectral tr iple, the starting point for the analysis of noncommutative spaces in the sense of Connes (1994), to the case where the algebra A contains b oth bosonic and fermionic degrees of freedom. The operator D of the sp ectral triple under consideration is the square root of the Dirac oper ator and thus the forms of the generalized differential algebra constr ucted out of the spectral triple are in a representation of the Lorent z group with integer spin if the form degree is even and half-integer spin if the form degree is odd. However, we find that the 2-forms, obt ained by squaring the connection, contain exactly the components of th e vector multiplet representation of the supersymmetry algebra. This a llows to construct an action for supersymmetric Yang-Mills theory in t he framework of noncommutative geometry.