The Anomalous Brst Resolution and Dirac Type Equations for High Spins

It is shown that the BRST resolution of the spaces of the physical states of high spin systems with anomalies can be consistently defined. The appropriate anomalous complexes are obtained by canonical restrictions of the ghost extended spaces to the kernel of curvature operator without any modifications of the “matter” sector. The cohomologies of the anomalous complex are calculated and analyzed in detail within the general framework of Hodge–deRham–Kähler theory: the vanishing theorem of relative cohomologies is proved and the absolute cohomologies are reconstructed. The Laplace operator determined by the anomaly is identified as the general spin irreducibility operator. The Dirac operator appears to be the restriction of the anomalous Laplace operator to the states of spin 1 2 . The diagonal matrix elements of the anomalous Laplace operator define the Lagrange densities describing the fields carrying arbitrarily high spin.