Date of Award

1-1-2020

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (vi, 69 pages)

Dissertation/Thesis Chair

Rongwei Yang

Committee Members

Rongwei Yang, Antun Milas, Marius Beceanu, Oleg Lunin

Keywords

C*-algebra, differential forms, Hodge star operator, Maxwell's equations, projective joint spectrum, Yang-Mills equations, Maxwell equations, Yang-Mills theory, Electromagnetic theory, C*-algebras, Gauge fields (Physics)

Subject Categories

Applied Mathematics | Mathematics | Physical Sciences and Mathematics

Abstract

Maxwell's equations, named after James C. Maxwell, are a U(1) gauge theory describing the interactions between electric and magnetic fields. They lie at the heart of classical electromagnetism and electrodynamics. Yang-Mills equations, named after C. N. Yang and Robert Mills, generalize Maxwell's equations and are associated with a non-abelian gauge theory called Yang-Mills theory. Yang-Mills theory unified the electroweak interaction with the strong interaction (QCD), and it is the foundation of the Standard Model in particle physics.

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