Asymptotically Non-Singular Extended Non-Dyonic Solutions of 't Hooft-Polyakov Monopole Violates Equations of Motion

Abstract

We show that based on the general solution, given by Corrigan, Olive, Fairlie and Nuyts, in the region outside the monopole's core; the equations of motion in the Higgs vacuum (i.e. outside the monopole's core) will not allow asymptotically non-singular extended non-trivial non-Dyonic (including, also, all static) solutions of the 't Hooft-Polyakov monopole. In other words, unless the monopole's magnetic charge is shielded (by some mechanism), the Dirac string is inevitable asymptotically, in the region outside the monopole's core, for all non-Dyonic solutions that are admissible by the equations of motion. That we show that the non-dyonic solutions (based on Corrigan et al) will include all "admissible" static solutions and their gauge transform might be interpreted as that all admissible dyonic solutions (based on Corrigan et al) are composite solutions.