Towards the deformation quantization of linearized gravity

TL;DR

This paper explores applying deformation quantization to linearized gravity, deriving quantum states and spectra from a Maxwell analogy, offering a novel approach to quantum gravity.

Contribution

It introduces a deformation quantization framework for linearized gravity using Maxwell analogies, providing a new method to quantize gravitational fields.

Findings

Derived quantum states for linearized gravity

Obtained a discrete spectrum for the quantum gravitational field

Established a deformation quantization procedure for free gravitational fields

Abstract

We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell Lagrangian which allows the construction of a Hamiltonian in the standard way. The deformation quantization procedure for free fields is applied to this Hamiltonian. As a result we obtain the complete set of quantum states and its discrete spectrum.