In this thesis, we revisit the calculation of matter quantum effects on the graviton self-energy on a flat Minkowski background, with the aim to acquire a deeper understanding of the mechanism that renders the graviton massless. We first review some essential background material of the framework of quantum field theory pertaining to the understanding of the classification of massless states on the Hilbert space. Using these techniques, along with the development of some preliminaries of general relativity, we show that the gravitational wave obtained through the linearised gravity equation must have only two polarisations of helicity $\sigma = \pm 2$; we infer that these correspond to massless graviton states of the same helicity. Then, by considering an Abelian Higgs model with minimal coupling to gravity, we argue that the graviton propagator obtained after radiative corrections must have a pole corresponding to the propagation of a massless particle if the graviton propagator is transverse. To show this transversality, we derive a new low-energy theorem which directly relates the radiative corrections of thecosmological constant to the longitudinal modes of the graviton self-energy to all orders in perturbation theory; we show this relation explicitly at the one-loop level. In the same Abelian Higgs model, we also calculate the matter quantum corrections to the Newtonian potential and present new formulae in terms of modified Bessel and Struve functions of the particle masses in the loop. We show that the correction to the Newtonian potential exponentially falls-off with the distance r, once the nonrelativistic limit with respect to the nonzero loop masses are carefully considered. For massless scalars, fermions, and gauge bosons in the loops, we recover the well-known results presented in the literature.

Matter Quantum Corrections in the Quantum Theory of Einstein Gravity

Burns, D. (Author). 1 Aug 2016

Student thesis: Phd