  In this note we give a BRST interpretation of inner product of group
averaging on de Sitter group SO(2,1). Quantization approaches can be divided in
two classes, without introducing additional degrees of freedom and with
introducing ghosts, antighosts, Lagrange multipliers and canonically conjugated
momenta. The first class of quantization methods includes Dirac method and
group averaging method. The Dirac method is based on imposing the constraint
conditions on physical states, while in group averaging method one modifies the
physical inner product due to constrains. One should distinguish the abelian
case for which you can have continuous spectrum and discrete spectrum for which
there are internal topological problems in BRST-BFV approach, and the
non-abelian case.
