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Extension of Chern-Simons forms and new gauge anomalies

We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher rank field-strength tensors. The integrals of these forms over the corresponding space-time coordinates provides new topological Lagrangians. With these Lagrangians one can define gauge field theories which generalize the Chern-Simons quantum field theory. We also present explicit expressions for the potential gauge anomalies associated with the tensor gauge fields and classify all possible anomalies that can appear in lower dimensions. Of special interest are those which can be constructed in four, six, eight and ten dimensions.