Superalgebraisation of BFV-BRST quantisation

In recent years it has been shown that, for the BFV-BRST extended phase-space quantisation of relativistic systems, hidden higher symmetry superalgebras are relevant. We examine the relationship between the BFV-BRST extended phase space construction for several cases and the structure of certain classes of representations of orthosymplectic superalgebras osp(D, 2/2) and their inhomogeneous extensions. Our motivation is to show, by way of several examples, how the hidden symmetry is manifested in the BFV-BRST method. In this class of superalgebras the physical particle states (that is, irreducible representations of the Poincare algebra, carried on appropriate types of relativistic wavefunctions) appear as the resolution of the BRST complex. This complex is naturally provided via an appropriate nilpotent odd generator (the BRST operator). Specific examples studied are the relativistic scalar and spinning particle, as well as a generalisation of the scalar particle in two dimensions, which we show to be associated with the exceptional superalgebra D(2, 1; a). This superalgebra is isomorphic to osp (2, 2/2) for a = 1.