# Nakanishi-Kugo-Ojima quantization of general relativity in Heisenberg picture

## TL;DR

This paper applies topological methods and the Nakanishi-Kugo-Ojima formalism to the canonical quantization of general relativity, ensuring unitarity and exploring nonrenormalizability within a novel framework.

## Contribution

It introduces a topological perspective to quantum gravity and performs canonical quantization in the Heisenberg picture using BRST symmetry, ensuring a consistent quantum framework.

## Key findings

- Existence of a topological invariant in gravity via Chern-Weil theory
- Construction of a BRST-invariant quantum gravity formalism
- Reconsideration of nonrenormalizability in this new formulation

## Abstract

The Chern-Weil topological theory is applied to a classical formulation of general relativity in four-dimensional spacetime. Einstein--Hilbert gravitational action is shown to be invariant with respect to a novel translation (co-translation) operator up to the total derivative; thus, a topological invariant of a second Chern class exists owing to Chern-Weil theory. Using topological insight, fundamental forms can be introduced as a principal bundle of the spacetime manifold. Canonical quantization of general relativity is performed in a Heisenberg picture using the Nakanishi-Kugo-Ojima formalism in which a complete set of quantum Lagrangian and BRST transformations including auxiliary and ghost fields is provided in a self-consistent manner. An appropriate Hilbert space and physical states are introduced into the theory, and the positivity of these physical states and the unitarity of the transition matrix are ensured according to the Kugo-Ojima theorem. The nonrenormalizability of quantum gravity is reconsidered under the formulation proposed herein.