Some problems with 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 raises some questions about the quantization procedure for a 't Hooft–Polyakov monopole.