TAILIEUCHUNG - Non-Abelian classical solution of the Yang-Mills-Higgs theory

In this paper, we investigate an SU(2) gauge field coupled with two massless Higgs triplets. We obtain a non-Abelian exact classical solution of corresponding Yang-Mills equations. We also find the energy expression of this classical solution. Some particular cases of the solution are considered. | JOURNAL OF SCIENCE OF HNUE Mathematical and Physical Sci. 2012 Vol. 57 No. 7 pp. 100-105 This paper is available online at http NON-ABELIAN CLASSICAL SOLUTION OF THE YANG-MILLS-HIGGS THEORY Nguyen Van Thuan Faculty of Physics Hanoi National University of Education Abstract. In this paper we investigate an SU 2 gauge field coupled with two massless Higgs triplets. We obtain a non-Abelian exact classical solution of corresponding Yang-Mills equations. We also find the energy expression of this classical solution. Some particular cases of the solution are considered. Keywords Non-Abelian gauge fields Higgs triplets Yang-Mills equation classical solution. 1. Introduction The Yang-Mills equations for the SU 2 gauge field coupled with the Higgs field suggest many interesting solution types monopole dyon instanton and meron 2 3 5 7 . Physical applications of the classical Yang-Mills-Higgs theory begin with exact solutions. The physical properties of monopoles dyons instantons and merons are particularly important. For example imaginary time solutions of classical theories are usually interpreted as real time tunneling in the corresponding quantized theory. Classical Yang-Mills-Higgs theory can be studied independently of exact solutions of course. This is an interesting parsuit because any results may lead to improvements in an integral formulation of quantum field theory 4 . The Yang-Mills equations are nonlinear differential equations. Exact solutions to nonlinear field theories are very difficult to find since there exists no general method for discovering them. The usual approach is to make some guess as to the form of the solution and insert it into the field equations to see if it solves them. For the Yang-Mills-Higgs theory there are some known exact solutions which are found by this approach 1 8 9 . Received July 25 2012. Accepted September 20 2012. Physics Subject Classification 60 44 01 03. Contact Nguyen Van Thuan e-mail address .

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