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.
The purpose of this thesis is, from a mathematical viewpoint, to derive a complex variable version of Maxwell's equations and Yang-Mills equations in connection with complex geometry, C*-algebras, projective joint spectrum, and Lie algebras. We shall consider working under the Euclidean metric, Minkowski metric, and a Hermitian metric g.
|Commitee:||Beceanu, Marius, Milas, Antun, Lunin, Oleg|
|School:||State University of New York at Albany|
|Department:||Mathematics and Statistics|
|School Location:||United States -- New York|
|Source:||DAI-B 81/12(E), Dissertation Abstracts International|
|Subjects:||Mathematics, Theoretical Mathematics, Applied Mathematics|
|Keywords:||C*-algebra, Differential forms, Hodge star operator, Maxwell's equations, Projective joint spectrum, Yang-Mills equations|
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