Quantum Gravity without General Relativity

TL;DR

This paper develops a quantum field theory of gravity based on Dirac fields coupled to electromagnetic and gravitational fields, avoiding reliance on Einstein's general relativity and proposing a renormalizable, massless graviton framework.

Contribution

It introduces a novel quantum gravity model using Dirac fields with gravitational coupling, independent of Einstein's equivalence principle, and provides a renormalization scheme ensuring a massless graviton.

Findings

Photon-gravity interaction strength is proportional to the electromagnetic coupling.

The model predicts gravity effects without Einstein's principle of equivalence.

A renormalization scheme maintains a massless graviton.

Abstract

The quantum field theory of gravitation is constructed in terms of Lagrangian density of Dirac fields which couple to the electromagnetic field $A_\mu$ as well as the gravitational field $\cal G$. The gravity appears in the mass term as $ m(1+g {\cal G}) \bar{\psi}\psi $ with the coupling constant of $g$. In addition to the gravitational force between fermions, the electromagnetic field $A_\mu$ interacts with the gravity as the fourth order effects and its strength amounts to $\alpha$ times the gravitational force. Therefore, the interaction of photon with gravity is not originated from Einstein's general relativity which is entirely dependent on the unphysical assumption of the principle of equivalence. Further, we present a renormalization scheme for the gravity and show that the graviton stays massless.