Chiral anomalies and the generalised index theorem

The paper shows that the generalised Atiyah-Singer index theorem describes not only the U(1) anomaly, but also the non-Abelian anomaly. The anomalies are determined in arbitrary even dimensions without ambiguity of coefficients. The index theorem reveals new kinds of anomalies. The relationship between these anomalies and the topology of Yang-Mills fields is discussed. (author)