NONCOMMUTATIVE GEOMETRY AND REALITY

We introduce the notion of real structure in our spectral geometry. Th is notion is motivated by Atiyah's KR-theory and by Tomita's involutio n J. It allows us to remove two unpleasant features of the ''Connes-Lo tt'' description of the standard model? namely, the use of bivector po tentials and the asymmetry in the Poincare duality and in the unimodul arity condition. (C) 1995 American Institute of Physics.