Poincar\'e charges for chiral membranes

TL;DR

This paper employs symplectic geometry to derive covariant conjugate variables, commutation relations, Poincaré charges, and the stress tensor for chiral superconducting membranes with null currents.

Contribution

It introduces a symplectic geometric approach to analyze the canonical structure and conserved charges of chiral membranes, which was not previously established.

Findings

Derived covariant conjugate variables for chiral membranes.

Established commutation relations and Poincaré charges.

Computed the stress tensor for the membrane theory.

Abstract

Using basic ideas of simplectic geometry, we find the covariant canonically conjugate variables, the commutation relations and the Poincar\'e charges for chiral superconducting membranes (with null currents), as well as we find the stress tensor for the theory under study.