Superhamiltonian formalism for $2D$ $N=1,2$ theories

TL;DR

This paper develops a supersymmetric Hamiltonian formalism for 2D N=1,2 theories using super-Poisson brackets on superfields, unifying physical and auxiliary fields in a boundary-condition-based approach.

Contribution

It introduces a novel superfield Hamiltonian framework for 2D supersymmetric theories that differs from previous light-cone formulations by treating dynamics through boundary conditions.

Findings

Formulates 2D N=1,2 supersymmetric theories in a manifestly supersymmetric Hamiltonian framework.

Unifies physical and auxiliary fields equations within the Hamiltonian formalism.

Provides a natural generalization of canonical Hamiltonian formalism for supersymmetric theories.

Abstract

We show how to formulate $2$-dimensional supersymmetric $N=1,2$ theories, both massive and conformal, within a manifestly supersymmetric hamiltonian framework, via the introduction of a (super)-Poisson brackets structure defined on superfields. In this approach, as distinct from the previously known superfield hamiltonian formulations, the dynamics 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 generalization of canonical hamiltonian formalism. One of its interesting features is that the physical and auxiliary fields equations appear on equal footing as the Hamilton ones.