Comment on Gravity and the Poincare Group

TL;DR

This paper discusses how two-dimensional gravity models can be reformulated as Poincare gauge theories, highlighting limitations related to diffeomorphism invariance and the reabsorption of modifications through variable changes.

Contribution

It demonstrates the reformulation of 2D gravity models into Poincare gauge theories and analyzes the constraints and limitations of this approach.

Findings

Reformulation of 2D gravity as Poincare gauge theory

Constraints remain complex despite reformulation

Modifications can be reabsorbed via variable changes

Abstract

Following the approach of Grignani and Nardelli [1], we show how to cast the two-dimensional model $L \sim curv^2 + torsion^2 + cosm.const$ -- and in fact any theory of gravity -- into the form of a Poincare gauge theory. By means of the above example we then clarify the limitations of this approach: The diffeomorphism invariance of the action still leads to a nasty constraint algebra. Moreover, by simple changes of variables (e.g. in a path integral) one can reabsorb all the modifications of the original theory.