Conserved Quasilocal Quantities and General Covariant Theories in Two Dimensions

TL;DR

This paper explores conserved quantities in 1+1 dimensional covariant theories, unifying various models through Poisson-sigma-models and analyzing the nature of quasilocal energy and momentum in these contexts.

Contribution

It provides a comprehensive discussion of conserved quantities and quasilocal energy in 1+1 dimensional covariant theories, including a generalization for matter interactions.

Findings

Unified description of conserved quantities across models

Relation between Noether charges and quasilocal energies clarified

Generalized conservation law for matter interactions presented

Abstract

General matterless--theories in 1+1 dimensions include dilaton gravity, Yang--Mills theory as well as non--Einsteinian gravity with dynamical torsion and higher power gravity, and even models of spherically symmetric d = 4 General Relativity. Their recent identification as special cases of 'Poisson--sigma--models' with simple general solution in an arbitrary gauge, allows a comprehensive discussion of the relation between the known absolutely conserved quantities in all those cases and Noether charges, resp. notions of quasilocal 'energy--momentum'. In contrast to Noether like quantities, quasilocal energy definitions require some sort of 'asymptotics' to allow an interpretation as a (gauge--independent) observable. Dilaton gravitation, although a little different in detail, shares this property with the other cases. We also present a simple generalization of the absolute conservation law for the case of interactions with matter of any type.