Hamiltonian Analysis of Non-Linear Sigma Model on Supercoset Target

TL;DR

This paper develops the Hamiltonian formulation for non-linear sigma models on supercoset targets, calculating Poisson brackets, equations of motion, and conserved charges to deepen understanding of their symmetries and dynamics.

Contribution

It provides a detailed Hamiltonian analysis of supercoset sigma models, including Poisson brackets and conserved charges, which was not comprehensively addressed before.

Findings

Computed Poisson brackets of left-invariant currents

Derived equations of motion for the currents

Identified conserved charges related to global symmetries

Abstract

This paper is devoted to the study of the Hamiltonian formulation of non-linear sigma models on supercoset targets. We calculate the Poisson brackets of left-invariant currents. Then we introduce the Hamiltonian of the system and determine the equations of motion for left-invariant currents. We also determine the charge corresponding to the invariance of the action under global left multiplication.