Author Type

Graduate Student

Date of Award

Spring 4-10-2026

Document Type

Dissertation

Publication Status

Version of Record

Submission Date

May 2026

Department

Physics

College Granting Degree

Charles E. Schmidt College of Science

Department Granting Degree

Physics

Degree Name

Doctor of Philosophy (PhD)

Thesis/Dissertation Advisor [Chair]

Jonathan Engle

Abstract

We begin with an introduction to canonical Loop Quantum Gravity. We then introduce a notion of residual diffeomorphism covariance in quantum Kantowski–Sachs (KS), describing the interior of a Schwarzschild black hole. We solve for the family of Hamiltonian constraint operators satisfying an associated covariance condition, as well as parity invariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naive) classical limit. We further explore imposing minimality of the number of momentum shift terms, and compare the solution with other Hamiltonian constraints proposed for Loop Quantum KS in the literature. In particular, we discuss a lapse recently commonly chosen due to the resulting decoupling of evolution of the two degrees of freedom and exact solubility of the model. We show that such a lapse choice can indeed be quantized as an operator densely defined on the Bohr Hilbert space, and that any such operator, when written as a linear combination of shift operators in the triad representation, must include an infinite number of terms. We then extend the KS framework to include a Maxwell field and repeat the classical part of the above analysis for this extended framework.

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