QUANTUM HAMILTONIAN REDUCTION IN SUPERSPACE FORMALISM

Recently the quantum hamiltonian reduction was done in the case of gen eral sl(2) embeddings into Lie algebras and superalgebras. In this pap er we extend the results to the quantum hamiltonian reduction of N = 1 affine Lie superalgebras in the superspace formalism. We show that if we choose a gauge for the supersymmetry, and consider only certain eq uivalence classes of fields, then our quantum hamiltonian reduction re duces to quantum hamiltonian reduction of non-supersymmetric Lie super algebras. We construct explicitly the super energy-momentum tenser, as well as all generators of spin 1 (and 1/2); thus we construct explici tly all generators in the superconformal, quasi-superconformal and Z(2 ) X Z(2) superconformal algebras.