Symmetry and Exact Solutions of the Maxwell and SU(2) Yang-Mills Equations

Details Symmetry and Exact Solutions of the Maxwell and SU(2) Yang-Mills Equations Symmetry and Exact Solutions of the Maxwell and SU(2) Yang-Mills Equations

2004-05-31

arxiv.org/abs/hep-th/0405286v1

Advances in Chemical Physics. Modern Nonlinear Optics, 2001, 119, part II, 269--352

Physics

High Energy Physics

High Energy Physics - Theory

81 pages, LaTeX

Scientific paper

We give the overview of solution techniques for the general conformally-invariant linear and nonlinear wave equations centered around the idea of dimensional reductions by their symmetry groups. The efficiency of these techniques is demonstrated on the examples of the SU(2) Yang-Mills and the vacuum Maxwell equations. For the Yang-Mills equations we have derived the most general form of the conformally-invariant solution and construct a number of their new analytical non-Abelian solutions in explicit form. We have completely solved the problem of symmetry reduction of the Maxwell equations by subgroups of the conformal group. This yields twelve multi-parameter families of their exact solutions, a majority of which are new and might be of considerable interest for applications.

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