Geometric Structure of Two Self-dual Fields with Constraints

TL;DR

This paper investigates the geometric structure of a two-dimensional self-dual field with constraints, deriving its symplectic form and conserved currents, all invariant under Poincaré transformations.

Contribution

It provides a geometric analysis of a constrained self-dual field, including symplectic structure and conserved quantities, expanding understanding of such fields in two dimensions.

Findings

Derived symplectic structure for the self-dual field

Identified conserved currents invariant under Poincaré group

Established geometric framework for constrained self-dual fields

Abstract

A two dimensional Poincar$\acute{e}$-invariant self-dual field with constraints is studied in geometric way. We obtained its symplectic structure and conservative currents on space of solutions, which are also invariant under transformations of Poincar$\acute{e}$ group.