# The canonical frame of purified gravity

## TL;DR

This paper discusses a novel formulation of gravity called purified gravity within Coincident General Relativity, highlighting its advantages in energy-momentum description, quantum path integrals, and canonical quantization.

## Contribution

It introduces a canonical frame for quantization and demonstrates improved energetics and thermodynamics in a torsion- and curvature-free gravity theory.

## Key findings

- Energy-momentum is locally conserved and symmetric.
- Euclidean path integral converges without boundary terms.
- A canonical frame for quantization is identified.

## Abstract

In the recently introduced gauge theory of translations, dubbed Coincident General Relativity, gravity is described with neither torsion nor curvature in the spacetime affine geometry. The action of the theory enjoys an enhanced symmetry and avoids the second derivatives that appear in the conventional Einstein-Hilbert action. While it implies the equivalent classical dynamics, the improved action principle can make a difference in considerations of energetics, thermodynamics, and quantum theory. This essay reports on possible progress in those three aspects of gravity theory. In the so-called purified gravity, 1) energy-momentum is described locally by a conserved, symmetric tensor, 2) the Euclidean path integral is convergent without the addition of boundary or regulating terms and 3) it is possible to identify a canonical frame for quantisation.