THE SPECTRAL ACTION PRINCIPLE

We propose a new action principle to be associated with a noncommutati ve space (A,H,D). The universal formula for the spectral action is (ps i, D psi) + Trace((chi)(D/Lambda)) where psi is a spinor on the Hilber t space, Lambda is a scale and (chi) a positive function. When this pr inciple is applied to the noncommutative space defined by the spectrum of the standard model one obtains the standard model action coupled t o Einstein plus Weyl gravity. There are relations between the gauge co upling constants identical to those of SU(5) as well as the Higgs self -coupling, to be taken at a fixed high energy scale.