General Relativity as the Classical Limit of the Renormalizable Gauge Theory of Volume Preserving Diffeomorphisms

TL;DR

This paper proposes a novel quantum gauge theory based on volume-preserving diffeomorphisms, which naturally leads to General Relativity as its classical limit when inertial and gravitational energies align.

Contribution

It introduces a new quantum gauge framework for gravity that differs from traditional approaches and derives General Relativity as its classical limit.

Findings

Classical General Relativity emerges from the gauge theory in the appropriate limit.

The theory distinguishes between inertial and gravitational energy-momentum at the quantum level.

A new symmetry group of spacetime transformations appears in the classical limit.

Abstract

The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an alternative approach to quantum gravity starts with the postulate that inertial and gravitational energy-momentum need not be the same for virtual quantum states. Separating their roles naturally leads to the quantum gauge field theory of volume-preserving diffeomorphisms of an inner four-dimensional space. The classical limit of this theory coupled to a quantized scalar field is derived for an on-shell particle where inertial and gravitational energy-momentum coincide. In that process the symmetry under volume-preserving diffeomorphisms disappears and a new symmetry group emerges: the group of coordinate transformations of four-dimensional spacetime and with it General Relativity coupled to a classical relativistic point particle.