Interaction of Non-Abelian Monopole with External Field

The interaction of a nontrivial topological field configuration with the external fields is considered. The approach is based on the calculation of the zero modes excitation probability. We consider the interaction of the t’Hooft-Polyakov monopole with an external weak uniform magnetic field and the field of another monopole. The t’Hooft-Polyakov non-Abelian monopole [1] are well-known static solutions of the nonlinear Yang-Mills-Higgs field equations. Though a considerable progress has been achieved in the last two decades, there are still open problems concerning the dynamical properties of monopoles. The most known results were obtained in the Bogomolny-Prasad-Sommerfield (BPS) limit [2] where the monopole dynamics changes drastically due to the masslessness of the scalar field. A calculation of the static force between two monopoles [3] and of the light scattering by a monopole [4] were based on an ansatz for the time dependence of the field which was just a replacement ~r → ~r− 1 2 ~at for the monopole position ~r, that was already corresponding to the monopole moving with a constant acceleration ~a. In Ref. [3] as well as in the following papers [5], [6], the interaction between the monopoles was considered in the region outside the monopole core where the Yang-Mills fields obey the free field equations. However, it resonable to expect a distortion of the core of the t’Hooft-Polyakov monopole and a bremstrahlung of both vector and scalar fields if the initially static monopole configuration is accelerated by an external field. ∗On leave of absence from the Institute of Physics, Minsk; Alexander von Humboldt fellow.