Browsing by Subject "asymptotic safety"

In this thesis a computation of the non-perturbative Lorentzian graviton propagator, which has appeared in the literature, is outlined. Firstly, the necessary ingredients for the computation are introduced and discussed. This includes; General Relativity (GR), its path integral quantisation around a Minkowski space background, and the definition of the graviton propagator along with its relation to the one-particle-irreducible (1PI) graviton 2-point function. A brief discussion on the perturbative non-renormalizability of the theory is followed by the introduction of the functional renormalization group (fRG) equation from which a fRG equation for the scalar coefficient function of the transverse-traceless (TT) 1PI graviton 2-point function is derived. After these ingredients have been introduced we proceed to outline the computation in question, skipping the details of its most involved steps. The computation starts by defining the spectral function and the Källén-Lehmann spectral representation of propagators. The non-perturbative TT 1PI graviton 2-point function, the propagators and the spectral functions, are parameterized and the fRG flow equation for the TT 1PI graviton 2-point function is used together with certain renormalization conditions to define renormalization group (RG) flow equations for these parameters. The solution of the flow of the parameters is displayed and is used to construct the graviton spectral function and the graviton propagator, which are both displayed graphically. Finally, a discussion of the features of the spectral function and propagator are given, and these results are briefly discussed in the context of the asymptotic safety program for quantum gravity and some of its open issues.