CHIRAL ANOMALY IN ASHTEKARS APPROACH TO CANONICAL GRAVITY

The Dirac equation in Riemann-Cartan spacetimes with torsion is recons idered. As is well-known, only the axial covector torsion A, a one-for m, couples to massive Dirac fields. Using diagrammatic techniques, we show that besides the familiar Riemannian term only the Pontrjagin typ e four-form dA boolean AND dA does arise additionally in the chiral an omaly, but not the Nieh-Yan term dA, as has been claimed recently. Im plications for cosmic strings in Einstein-Cartan theory as well as for Ashtekar's canonical approach to quantum gravity are discussed.