General Superfield Quantization Method. II. General Superfield Theory of Fields: Hamiltonian Formalism

Abstract

In the framework of started in Ref.[1] construction procedure of the general superfield quantization method for gauge theories in Lagrangian formalism the rules for Hamiltonian formulation of general superfield theory of fields (GSTF) are introduced and are on the whole considered. Mathematical means developed in [1] for Lagrangian formulation of GSTF are extended to use in Hamiltonian one. Hamiltonization for Lagrangian formulation of GSTF via Legendre transform of superfunction $S_{L}\bigl({\cal A}(\theta),{\stackrel{\circ}{\cal A}}(\theta),\theta\bigr)$ with respect to ${\stackrel{\circ}{{\cal A}^{\imath}}}(\theta)$ is considered. As result on the space $T^{\ast}_{odd}{\cal M}_{cl}\times \{\theta\}$ parametrized by classical superfields ${\cal A}^{\imath}(\theta)$, superantifields ${\cal A}^{\ast}_{\imath}(\theta)$ and odd Grassmann variable $\theta$ the superfunction $S_{H}({\cal A}(\theta),{\cal A}^{\ast}(\theta),\theta)$ is defined. Being equivalent to different types of Euler-Lagrange equations the distinct Hamiltonian systems are investigated. Translations along $\theta$ for superfunctions on $T^{\ast}_{odd}{\cal M}_{cl}\times \{\theta\}$ being associated with these systems are studied. Various types of antibrackets and differential operators acting on $C^{k}\bigl(T^{\ast}_{odd}{\cal M}_{cl} \times \{\theta\} \bigr)$ are considered. Component (on $\theta$)formulation for GSTF quantities and operations is produced. Analogy between ordinary Hamiltonian classical mechanics and GSTF in Hamiltonian formulation is proposed. Realization of the GSTF general scheme is demonstrated on 6 models.