Date of Award
Ph.D. in Physics
Causal set theory is an approach to quantum gravity which replaces the continuous spacetime manifold with a discrete set of points and a partial order. In this work, I will focus on causal sets embeddable in two-dimensional manifolds, and define an action based on chains which in the continuum limit replicates the Einstein-Hilbert action; furthermore, I will propose a variational principle based on this action and numerically show it can distinguish nonflat manifoldlike causal sets from the most common type of nonmanifoldlike causal sets. I will then supplement this action with a boundary term similar to the Gibbons-Hawking-York boundary term completing the treatment of two-dimensional causal sets. Finally, I will explore quantum scalar fields on causal sets though the back reaction on the causal set due to the stress-energy tensor of the scalar field is ignored (this is analogous to what is done in quantum field theory in the continuum) via a simple model of a particle detector travelling on a "geodesic" in the causal set.
Pilgrim, Benjamin, "Dynamics for Discretized Gravity in the Causal Set Approach" (2021). Electronic Theses and Dissertations. 2128.