BRST Symmetry and Cohomology

We present the mathematical considerations which determine all gauge invariant ac-tions and anomaly candidates in gauge theories of standard type such as ordinary or gravitational Yang Mills theories. Starting from elementary concepts of field theory the discussion tries to be explicit and complete, only the cohomology of simple Lie algebras it quoted from the literature. After a short introduction to jet spaces chapter 1 deals with the “raison d’être ” of gauge symmetries: the problem to define the subspace of physical states in a Lorentz invariant theory with higher spin. The operator Qs which characterizes the physical states was found by Carlo Becchi, Alain Rouet and Raymond Stora as a symmetry generator of a fermionic symmetry, the brst symmetry, in gauge theories with covariant gauge fixing [1]. Independently Igor Tjutin described the symmetry in a Lebedev Institute report which however remained unpublished for political reasons. For a derivation of the brst symmetry from the gauge fixing in path integrals the reader may consult the literature [2, 4, 21]. Chapter 1 is supplemented by a discussion of free vectorfields for gauge parameter λ 6 = 1. This is not a completely trivial exercise [3] and rarely discussed i