The Space of Solutions of Toda Field Theory

TL;DR

This paper introduces a new parameterisation for solutions of Toda field theory, explores its phase space structure, and extends the results to non-Abelian cases, providing a comprehensive mathematical framework.

Contribution

It presents a novel parameterisation of Toda solutions, analyzes the phase space structure, and extends findings to non-Abelian Toda theories.

Findings

New parameterisation of Toda solutions

Isomorphism between covariant and Hamiltonian phase spaces

Extension of methods to non-Abelian Toda theories

Abstract

A new parameterisation of the solutions of Toda field theory is introduced. In this parameterisation, the solutions of the field equations are real, well-defined functions on space-time, which is taken to be two-dimensional Minkowski space or a cylinder. The global structure of the covariant phase space of Toda theory is examined and it is shown that it is isomorphic to the Hamiltonian phase space. The Poisson brackets of Toda theory are then calculated. Finally, using the methods developed to study the Toda theory, we extend these results to the non-Abelian Toda field theories.