Internal force distributions in the ’t Hooft-Polyakov monopole and Julia-Zee dyon

Abstract

The energy-momentum tensor (EMT) of the 't Hooft-Polyakov monopole and the Julia-Zee dyon are studied. This tensor contains important information about the pressure and the shear force distributions which define mechanical properties of systems. Obtaining the violation of the local stability criterion for the magnetic monopole and dyon we decompose the EMTs into the long- and short-range parts. This decomposition depends on the Abelian field strength tensor which cannot be uniquely defined. We suggest to use the modified 't Hooft definition for the tensor. Finally, the long- and short-range parts of the EMTs are computed and new equilibrium equations are obtained. Numerical values for masses, $D$-terms, and various mean square radii for the monopole and the dyon are also computed.