EXTENDED SUPERCONFORMAL ALGEBRAS AND FREE-FIELD REALIZATIONS FROM HAMILTONIAN REDUCTION

We develop the method of the hamiltonian reduction of affine Lie super algebras to obtain explicit and general expressions both for the class ical and the quantum extended superconformal algebras. By performing t he gauge transformation which connects the diagonal gauge with the Dri nfeld-Sokolov gauge and considering the quantum corrections, we get ge neric expressions for the classical and quantum free field realization s of the algebras. Finally we give the expressions for the screening o perators, necessary for the development of the representation theory o f the extended superconformal algebras.