SUPERHAMILTONIAN FORMALISM FOR 2D N=1,2 THEORIES

We show how to formulate two-dimensional (2D) supersymmetric N = 1, 2 theories, both massive and conformal, within a manifestly supersymmetr ic Hamiltonian framework, via the introduction of a (super)-Poisson br ackets structure defined on superfields. In this approach, as distinct from the previously known superfield Hamiltonian formulations, the dy namics is not separated into two unrelated 2D light-cone superspaces, but is recovered by specifying boundary conditions at a given ''super- time'' coordinate. So the approach proposed provides a natural general ization of canonical Hamiltonian formalism. One of its interesting fea tures is that the physical and auxiliary fields equations appear on eq ual footing as the Hamilton ones.