Path Integral Quantization of Lorentz Gauge Theory of Gravity: With a Proof of Unitarity and Full Renormalizability in the Vacuum

TL;DR

This paper demonstrates that a spinless, vacuum gravity theory can be formulated as a Yang-Mills theory, proving its unitarity and renormalizability through path integral quantization, extending the standard model framework.

Contribution

It introduces a path integral quantization of the spinless gravity theory, establishing its unitarity and renormalizability in vacuum, and clarifies the theory's relation to Yang-Mills frameworks.

Findings

Spinless gravity in vacuum is equivalent to a Yang-Mills theory.

The theory is proven to be unitary and renormalizable to all orders.

Path integral formulation and Feynman rules are developed.

Abstract

We show that a spinless theory of gravity is also allowed by the kinematics of general relativity. In the absence of fermions the spinless theory of gravity and the theories in the standard model of particle physics are the same Yang-Mills theories with different gauge groups. Therefore, every theorem of a pure Yang-Mills theory is valid for the spinless theory of gravity in vacuum, i.e. it is unitary and renormalizable to all orders. When fermions are present the spinless theory of gravity has an extra constraint due to the tetrad postulate. A path integral quantization of this theory and all the Feynman rules are presented.