Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations

Abstract

We show that ghosts in gauge theories can be interpreted as Maurer-Cartan forms in the infinite dimensional group ^ of gauge transformations. We examine the cohomology of the Lie algebra of ^ and identify the coboundary operator with the BRS operator. We describe the anomalous terms encountered in the renormalization of gauge theories (triangle anomalies) as elements of these cohomology groups.

E 7(7) symmetry in perturbatively quantised $ \mathcal{N} = 8 $ supergravity

“…The anomalies associated to a linearly realised group are well known, and are classified by symmetric Casimirs. A nice way to derive such anomalies is by means of the 'Russian formula' [36][37][38][39] 29) to derive a (d + δ k )-cocycle from any symmetric Casimirs by use of the Cartan homotopy formula. In four dimensions, the relevant Casimir is the symmetric tensor of rank three, and the Cartan homotopy formula gives…”

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