Abstracts

George Savvidy

Extension of Chern-Simons forms

We investigate metric independent, gauge invariant, and closed forms in the generalized Yang-Mills (YM) theory. These forms are polynomial on the corresponding fields strength tensors ??? curvature forms and are analogous to the Pontryagin-Chern densities in the YM gauge theory. The corresponding secondary characteristic classes have been expressed in integral form in analogy with the Chern-Simons form. Because they are not unique, the secondary forms can be dramatically simplified by the addition of properly chosen differentials of one-step-lower-order forms. Their gauge variation can also be found yielding the potential anomalies in the gauge field theory.