Discovering Two Novel Solutions: Circular and Hyperbolic Functions of SU(2) Yang-Mills Gauge Field Equations Using Null-Tetrad Formalism

Abstract

Two more new exact closed-form solutions of SU(2) Yang-Mills gauge field equations were found by the Carmeli-Charash-Kaye-Kh. Huleihil null-tetrad formalism. Unlike the reported first solutions with special functions of elliptic integrals, these new solutions are circular and hyperbolic trigonometric functions with two arbitrary integration constants. Electric parts corresponding to the solutions with circular functions cases are found as zero and nonzero magnetic parts so concluded as monopole solutions. In solutions with hyperbolic function cases, both electric and magnetic parts of Yang-Mills fields are zero.  Yang-Mills potentials and fields are also reported for all solutions.