Consistent and covariant Schwinger terms in anomalous gauge theories

The field-theoretical method initiated by Wess lies at the heart of our considerations. In its original form, it was developed to derive the consistent Schwinger terms from the given expression of the consistent anomaly. First of all we formulate this method in appropriate differential geometrical setting. The method will be reviewed in the consistent case. Finally the consistent Schwinger terms were calculated in two and four dimensions. One of the main results is a new geometrical interpretation for the covariant anomaly and the Bardeen-Zumino functional. This functional can be viewed as a connenction of a line bundle over the space of all gauge potentials. The meaning of the internal U(1)-gauge freedom is elucidated and a modified consistency condition is formulated for the covariant anomaly. This differential geometrical interpretation enables us to extend the method of Wess to calculate covariant Schwinger terms from the known form of the covariant anomaly. Finally these Schwinger terms were calculated in two and four dimension. Furthermore, the applicability of the Wess method is discussed for the gravitational case. In two dimensions we recover the known results. By the way we find an explicit formula for all components of the Schwinger term. In dimensions n>2 we identify those components, which can be obtained by the method of Wess