Open Collections

Berean-Dutcher, Jonah

University of British Columbia

Matrix quantum mechanics provides an example of spacetime emergence where the underlying system is non-geometric. Understanding the mechanism for this emergence, and the way in which entanglement between the quantum mechanical degrees of freedom relates to the emergent field theory, remains a key challenge in quantum gravity. Previous work has examined this relation in the context of a single matrix theory, and its emergent theory upon the noncommutative sphere. By using direct calculations of entanglement entropy of the matrix degrees of freedom, construction of the emergent fuzzy geometry is examined. This thesis attempts to extend this work to the case of a three matrix theory. The theory contains gauge-invariance, and a possible prescription is explored for restricting the full theory to the gauge-invariant configuration space. The implications for locality in the emergent theory, and thus potential for entanglement entropy definition, are evaluated and discussed.

Text

2022-08-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/82544

Physics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/