The Existence Of Self-Dual Non-Abelian Vortices In A Ф~2 Chern-Simons Gauge Theory

Gauge field theories present a rich spectrum of finite energy classical solution; such as vortices,monopoles and instantons.These classical solutions can be classified as topological or non-topological;depending of the origin of the stability mechanism. Among these theories,the self-dual theories deserve special attention.Our example originates from a non-Abelian Chern-Simons theory in A.Antillon, J.Escalona,G.German and M.Torres for which the gauge-covariant derivatives contain an anomalous interaction and the Higgs potential density is of a quadratic type,which also appears in an Abelian version of the model of a similar structure proposed by M.Torres in 1992.The thesis mainly concern with the existence of vortex solutions to the self-dual equation in the non-Abelian Chern-Simons gauge theory.We shall prove the existence of non-topological radially symmetric solutions according to A.Antillon,J.Escalona,G.German and M.Torres.The background of the problems we concerned is introduced in chapter 1.The main results of the thesis are also given in this chapter.In chapter 2.we point out the error equation in[1]and prove the non-existence of the solutions for the equation in[1].In chapter 3,some sufficient conditions are obtained for the existence of nontopological radially symmetric n-vortex solutions for the self-dual equation which we have amended by using the shooting method.In chapter 4.the radially symmetry property of the bare solutions is studied by using the moving plane method and finally some results are obtained for the bare solutions.