The Solutions of Affine and Conformal Affine Toda Field Theories

TL;DR

This paper presents new formulations for solutions of affine and conformal affine Toda field theories, detailing their parameterization, phase space structure, and static solutions.

Contribution

It introduces novel formulations of solutions, describes their phase space, and derives fundamental Poisson brackets for these theories.

Findings

Solutions parameterized by initial data

Phase spaces are diffeomorphic to Hamiltonian ones

Explicit static solutions for affine theory

Abstract

We give new formulations of the solutions of the field equations of the affine Toda and conformal affine Toda theories on a cylinder and two-dimensional Minkowski space-time. These solutions are parameterised in terms of initial data and the resulting covariant phase spaces are diffeomorphic to the Hamiltonian ones. We derive the fundamental Poisson brackets of the parameters of the solutions and give the general static solutions for the affine theory.