Application of Harmonic Maps $CP^{(N-1)}$ on SU(N) Bogomolny Equation for BPS Magnetic Monopoles

In this thesis we study dynamic of magnetic monopoles from Lagrangian density in Yang-Mills-Higgs field theory. In particular, we discuss BPS (Bogomolny Prasad Sommerfield) magnetic monopoles, described by SU(N) Bogomolny equations, which has field equations in form of non-linear coupled matrix field equations. One of the methods to simplify SU(N) Bogomolny equations is by using harmonic maps $CP^{(N-1)}$. This method has relation with $Gr(n,N)} σ$-model and can transform SU(N) Bogomolny equation into more simple scalar field equations that depends only on one variable. As an example, we consider the case of SU(2) Bogomolny equation.

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