45∘ Relative Orientations of Planes of Polarizations States of Gravitational Waves and the Graviton

The recent detection of gravitational waves calls for, not just in words or by plausible arguments, of an explicit derivation of polarization aspects of gravitational waves with emphasis, especially, on the non-trivial aspect of the relative 45 ∘ orientations of the planes of polarization states of gravitation in the same way as has been done over the years for the far simpler case involving electromagnetic wave propagation with the well known relative 90 ∘ between its polarization states. The purpose of this communication is to carry out in a covariant description as well as by giving special attention to the underlying gauge problem these polarization aspects via a direct consideration of the graviton propagator in a quantum field theory setting from which fundamental properties of polarizations are readily extracted.