The Einstein-Hilbert Lagrangian Density in a 2-dimensional Spacetime is an Exact Differential

TL;DR

This paper clarifies whether the Einstein-Hilbert Lagrangian in 2D spacetime can be expressed as an exact differential, resolving conflicting claims in the literature using Clifford bundle formalism.

Contribution

The paper provides a simple proof using Clifford bundle formalism that clarifies the nature of the Einstein-Hilbert Lagrangian in 2D spacetime.

Findings

The Einstein-Hilbert Lagrangian in 2D is an exact differential.

The paper resolves conflicting claims about the Lagrangian's form.

It demonstrates the correctness of previous statements by Deser and Jackiw.

Abstract

Recently Kiriushcheva and Kuzmin claimed to have shown that the Einstein-Hilbert Lagrangian cannot be written in any coordinate gauge as an exact differential in a 2-dimensional spacetime. Since this is contrary to other statements on the subject found in the literature, as e.g., by Deser and Jackiw, Jackiw, Grumiller, Kummer and Vassilevich it is necessary to do decide who has reason. This is done in this paper in a very simply way using the Clifford bundle formalism. In this version we added Section 18 which discusses a recent comment on our paper just posted by Kiriushcheva and Kuzmin.