Date of Award:
8-2025
Document Type:
Dissertation
Degree Name:
Doctor of Philosophy (PhD)
Department:
Physics
Committee Chair(s)
Charles G. Torre
Committee
Charles G. Torre
Committee
James T. Wheeler
Committee
Mark E. Fels
Committee
Oscar Varela
Committee
D. Mark Riffe
Abstract
In physics, symmetries help us understand complex systems by revealing conserved quantities and simplifying equations. In the context of general relativity, where spacetime is curved and dynamic, these symmetries become especially important when trying to reduce or solve the equations that govern gravitational and matter fields.
This dissertation investigates a mathematical principle known as the Principle of Symmetric Criticality (PSC), which helps determine when symmetries can be used to simplify physical theories without losing essential information. While often assumed to be valid, PSC does not always hold, and understanding when it does is critical for the reliable use of symmetry in theoretical physics.
The first part of this work identifies all possible spacetime symmetries that allow such simplification for gravitational fields, specifically within Einstein’s theory. The second part introduces a new method for choosing coordinate conditions, or “gauge fixing,” when working with simplified versions of the equations. An important step for both theoretical understanding and computational modeling. Finally, the third part extends these ideas to spinor fields, which describe particles like electrons and are essential in quantum field theory. This extension uses a two-component spinor formalism adapted to curved spacetime, showing that the same symmetry criteria used for gravitational fields also apply to spinor fields.
To support these results, custom computer code was written to automate the complex symbolic calculations involved. Together, the findings offer new tools and insights for researchers studying symmetry, gravity, and the mathematical foundations of field theory.
Checksum
eccf704f44b4198bd5d6ef76044931cb
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Recommended Citation
Frausto, Guillermo, "An Investigation Into the Principle of Symmetric Criticality" (2025). All Graduate Theses and Dissertations, Fall 2023 to Present. 539.
https://digitalcommons.usu.edu/etd2023/539
Included in
Copyright for this work is retained by the student. If you have any questions regarding the inclusion of this work in the Digital Commons, please email us at .