Date of Award

5-12-2024

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Advisor(s)

John Laiho

Keywords

Correlator;Effective field theory;Euclidean;Gravity;Quantum

Subject Categories

Physical Sciences and Mathematics | Physics | Quantum Physics

Abstract

Recent successes in Euclidean Dynamical Triangulations (EDT) motivate the further comparison of lattice observables to predictions of general relativity (GR) treated as an effective quantum theory. A particularly promising observable is the two-point function of the scalar curvature, which can be straightforwardly computed on the lattice and which in principle can also be computed from the Einstein-Hilbert path integral. Any such comparison should be between manifestly gauge-invariant observables, and will require that the GR predictions be analytically continued in a gauge-invariant manner to the Euclidean signature of the lattice. In this thesis I present my work toward this goal, namely: the construction of a set of relational observables, including the scalar invariantized scalar curvature; the calculation of the graviton propagator in a basis suitable for continuation; and the calculation of three manifestly gauge-invariant results in Lorentzian signature, as support of the coherence of the so-far developed machinery. I conclude by outlining the difficulties that remain in the evaluation of the scalar curvature two-point function at one loop, including the stubborn gauge dependence of the result and the difficulty in actually performing the analytic continuation to Euclidean signature.

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Open Access

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