The σ_ Cohomology Analysis for Symmetric Higher-Spin Fields

In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective sigma_ cohomology both in the tensor language in Minkowski space of any dimension and in terms of spinors in AdS(4). In the d-dimensional case Hp(sigma_) is computed for any p and interpretation of Hp(sigma_)is given both for the original Fronsdal system and for the associated systems of higher form fields.