What Is the Spin of a 't Hooft-Polyakov Magnetic Monopole?

[pxb]

Hi there,

I was wondering what is the spin of a magnetic monopole. To be specific, I mean the 't Hooft-Polyakov monopole in the Georgi-Glashow model. Sure, it is a purely classical object and as far as I know, there is no known way how to fully quantize it. So, strictly speaking, the notion of spin makes no sense here. But anyway, were it quantized, aren't there any arguments for what spin it would have?

Furthermore, the 't Hooft-Polyakov monopole has the winding number n=1. Considering solutions with higher n, would there be any n-dependence of the spin? For instance, couldn't be the spin proportional to n?

 

[AndyW]

Hello,

Thank you for your interesting question! The concept of spin is usually associated with particles, which have a point-like nature. However, the 't Hooft-Polyakov monopole is a topological soliton, which means it has a extended structure and cannot be described as a point-like object. This is why the concept of spin does not apply to it in the classical sense.

In terms of quantization, as you mentioned, there is currently no known way to fully quantize the 't Hooft-Polyakov monopole. However, there have been some theoretical attempts to describe its properties in terms of a quantum field theory, such as the Georgi-Glashow model you mentioned. In these theories, the monopole is described as a composite object made up of gauge bosons and Higgs particles. In this context, the spin of the monopole would be determined by the spin of these constituent particles and their interactions.

As for the winding number n, it is possible that the spin could be related to it in some way. However, this would depend on the specific theory used to describe the monopole and its interactions. Without a fully quantized theory, it is difficult to make any definitive statements about the relationship between spin and winding number.

In conclusion, while the concept of spin may not directly apply to the 't Hooft-Polyakov monopole, it is possible that it could be determined by the properties of its constituent particles and their interactions. Further research and development in the field of quantum field theory may provide more insight into this question in the future. Thank you for bringing this topic to our attention.