Anomalies and cohomologies
Anomaly is an object in the quantum theory of fields, physicists like fancy words. Field Theory is a system with infinite number of degrees of freedom and upon quantisation some symmetries break down. This is called anomaly.I will argue that in the case of the Yang-Mills theory the symmetry is not broken but is rather modified. Group action is supplied with a factor and/or is substituted by a projective presentation. Corresponding one and two cocycles are produced by the Chern-Simons descent procedure starting from the third Chern class.
Early Yang-Mills theories. Higgs Hunting 2013
Ludwig Dmitrievich Faddeev Steklov Mathematical Institute 23 Nov 2010, TIFR, Mumbai