Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2021
Committee Chair or Co-Chairs
Jeff Knisley
Committee Members
Rodney Keaton, Robert Gardner
Abstract
While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to zeta function regularization and explore more fully the relationship between operators in physics and classical zeta functions of mathematics. In so doing, we highlight intriguing connections to number theory that arise.
Document Type
Thesis - unrestricted
Recommended Citation
Wang, Stephen, "Zeta Function Regularization and its Relationship to Number Theory" (2021). Electronic Theses and Dissertations. Paper 3895. https://dc.etsu.edu/etd/3895
Copyright
Copyright by the authors.
Included in
Analysis Commons, Number Theory Commons, Other Applied Mathematics Commons, Other Mathematics Commons, Probability Commons, Quantum Physics Commons