An elliptic complex associated to the Yang-Mills constraint equations (original) (raw)

MAXWELL'S EQUATIONS AND YANG-MILLS EQUATIONS IN COMPLEX VARIABLES: NEW PERSPECTIVES

2020

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.

Derivation of Yang-Mills equations from Maxwell Equations and Exact solutions

Journal of Advances in Mathematics, 2013

In this paper we derived the Yang-Mills equations from Maxwell equations. Consequent-ly we find a new form for self-duality equations. In addition exact solution class of the classical SU(2) Yang-Mills field equations in four dimensional Euclidean space and two exact solution classes for SU(2) Yang- Mills equations when is a complex analytic function are also obtained.