Poisson Structure Induced (Topological) Field Theories

TL;DR

This paper introduces a class of two-dimensional field theories derived from Poisson structures, providing classical solutions and a Hamiltonian quantization scheme, thereby generalizing gravity-Yang-Mills systems.

Contribution

It presents a new class of 2D field theories based on Poisson structures, with explicit classical solutions and a Hamiltonian quantization framework.

Findings

Classical solutions of the models are explicitly given.

A general scheme for quantization in Hamiltonian form is developed.

The models generalize gravity-Yang-Mills systems.

Abstract

A class of two dimensional field theories, based on (generically degenerate) Poisson structures and generalizing gravity-Yang-Mills systems, is presented. Locally, the solutions of the classical equations of motion are given. A general scheme for the quantization of the models in a Hamiltonian formulation is found.