ENERGY-LEVELS OF THE MAGNETIC MONOPOLE IN THE PRASAD-SOMMERFIELD LIMIT

By analyzing the asymptotic behavior of the 't Hooft magnetic monopole in the Prasad-Sommerfield limit we see that there is no uniqueness of the finite-energy solution due to one degree of freedom recovered. Moreover, this degree of freedom should be quantized in order to get a finite-energy solution. Having at our disposal the asymptotic form of solutions at r0 and r, we match them up at some finite value r=a in a C0-class way, then insert the result into the energy integral and find the minimum with respect to the parameter a. Thus we find the approximate energy levels of the monopole in the Prasad-Sommerfield limit. © 1979 The American Physical Society.