Quantization and bosonic BRST theory (Q810961)

The authors study the problem of the quantization of a system with first class constraints. The simplest case to consider is that of a constrained classical system with symmetry which may be described by means of a symplectic manifold (M,\(\omega\)) with a free and proper Hamiltonian action of a connected Lie group G. The authors examine the conditions under which the quantizations of the original phase space M and reduced phase space \(\bar M\) (obtained by imposing the constraints classically) are compatible. One obstruction is the unimodularity of G. In this paper it is shown how the unimodularity obstruction may be avoided using a purely bosonic version of the classical BRST theory. The key observation here is that the BRST symmetry has a natural bosonic analogue in symplectic geometry and the BRST charge appears as component of an ordinary momentum mapping on an extended symplectic phase space (obtained by adjoining ghost-antighost canonical pairs in natural way).