Principles of BRST quantization

The BRST quantization as a quantization method is analyzed. It is pointed out that all formal manipulations are only valid if all inner products in the original state space are finite. This restriction is also shown to be necessary in order to obtain the correct results for trivial models. It is argued that the investigations of BRST invariant states of the form vertical strokeM>vertical strokeG>, where M and G denote matter and ghost states, are sufficient to determine the physics of the BRST invariant subspace. A prescription of how to solve Qvertical strokeM>vertical strokeG>=0 is given for a general class of models. Solutions are classified into canonical and noncanonical ones. The latter cannot be obtained in a canonical quantization of the corresponding gauge model. (orig.)