Date of Award
5-2025
Degree Type
Report
Degree Name
Master of Science (MS)
Department
Physics
Committee Chair(s)
Charles Torre (Committee Chair)
Committee
Charles Torre
Committee
Jim Wheeler
Committee
Mark Fels
Abstract
Physics seeks to understand the universe by uncovering the fundamental laws that govern matter, energy, space, and time. At its heart lies the challenge of unification: finding a mathematical framework that consistently describes these interactions across all scales, from the subatomic to the cosmological.
This thesis explores geometric algebra, a mathematical language that unifies algebra and geometry, as a tool for advancing this understanding. By extending this framework to curved spacetimes, where gravity influences the structure of space and time, we investigate its ability to describe physical phenomena such as electromagnetism and general relativity. A notable contribution includes the geometric algebraic treatment of physical units and dimensional analysis, whereby time, space, mass, charge, energy, and more are all incorporated directly into the mathematical framework.
Another key part of this work develops geometric calculus, a generalization of differentiation and integration, to study multivector fields in curved spaces. This allows us to represent Maxwell’s equations, which govern electromagnetism, in a compact and elegant form across different spacetime dimensions. The methods are then applied to analyze electrodynamics in a (2+1)-dimensional spacetime, offering insights into the true nature of electric and magnetic fields.
By merging physical principles with advanced mathematics, this thesis contributes to the ongoing search for frameworks that bridge the gap between classical and modern physics. The results suggest that geometric algebra holds promise for simplifying and unifying descriptions of physical laws, offering a powerful new lens for deeper insights into the fundamental nature of the universe.
Recommended Citation
Rhine, Kevin, "Geometric Algebra for Field Theory in Curved Spacetime" (2025). All Graduate Reports and Creative Projects, Fall 2023 to Present. 76.
https://digitalcommons.usu.edu/gradreports2023/76
Included in
Algebra Commons, Elementary Particles and Fields and String Theory Commons, Geometry and Topology Commons, Other Mathematics Commons, Other Physics Commons
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