A new approach to BRST operator cohomologies: Exact results for the BRST-fock theories

The modification of the BRST approach suggested by the authors and based on using the Lie superalgebra \hbox {$l\mkern 2mu(1,1)$} as the full algebra of the BRST symmetry is applied to the problem of calculating BRST operator cohomologies. The calculation is done for the class of BRST–Fock theories. The operator cohomologies are proved to be trivial. The result is interpreted as the analog of the no-ghost theorem on the level of observables.