ON THE CHIRAL ANOMALY IN NON-RIEMANNIAN SPACETIMES

The translational Chern-Simons type three-form coframe boolean AND tor sion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan four-form. Following Chandia and Zanelli, two spaces with nontrivial translational Chern-Simons forms are discussed. We then de monstrate, first within the classical Einstein-Cartan-Dirac theory and second in the quantum heat kernel approach to the Dirac operator, her o the Nieh-Yan form surfaces in both contexts, in contrast to what has been assumed previously.