Quantum Field Theory with Classical Sources - Linearized Quantum Gravity

TL;DR

This paper extends a quantum-mechanical framework from electromagnetism to linearized gravity, deriving classical gravitational equations and phenomena like quadrupole radiation from quantum principles.

Contribution

It introduces a quantum framework for linearized gravity that naturally yields classical Einstein equations and gravitational radiation, bridging quantum and classical descriptions.

Findings

Derivation of classical linearized Einstein equations from quantum expectations.

Explanation of gravitational quadrupole radiation within the quantum framework.

Insight into microscopic graviton emission and absorption processes.

Abstract

In a previous work and in terms of an exact quantum-mechanical framework, $\hbar$-independent causal and retarded expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge were derived in the presence of a conserved classical electric current. The classical $\hbar$-independent Maxwell's equations then naturally emerged. In the present work, we extend these considerations to linear gravitational quantum deviations around a flat Minkowski space-time in a Coulomb-like gauge. The emergence of the classical causal and properly retarded linearized classical theory of general relativity with a conserved classical energy-momentum tensor is then outlined. The quantum-mechanical framework also provides for a simple approach to classical quadrupole gravitational radiation of Einstein and microscopic spontaneous graviton emission and/or absorption processes.