Quantum field theory with classical sources-linearized quantum gravity

In a previous work (Skagerstam 2018 arXiv:1801.09947v1 [quant-ph]) and in terms of an exact quantum-mechanical framework, -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 -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.