Some problems when calculating the quantum corrections to the classical 't Hooft-Polyakov monopole

Abstract

We examine whether the analysis of quantum corrections for the kink soliton carries over to the 't Hooft-Polyakov monopole. For the kink, it is central that the quantum fluctuations are eigenmodes of a Hermitian operator. For the monopole, we show the analogous operator is not Hermitian. This property raises some questions about the quantization procedure for a 't Hooft-Polyakov monopole.