Uniqueness and Stability of Monopole Solutions in Classical Non-Abelian Gauge Field Theories.
The spectrum of magnetic monopoles in two different classical gauge theories is investigated, starting with the SO(3) electro-weak theory of Georgi. This theory's lowest charge, pure magnetic monopole solution has been studied extensively and is known to be unique, at least in the Prasad-Sommerfield limit and probably away from this limit as well. In the dyon case it has been conjectured that there may be other solutions beyond the one known. It is proved here that the radial functions describing the electric and magnetic fields must differ by only an overall constant, hence simplifying greatly the search for new dyons. It is then firmly established that the known lowest charge dyon is also unique, at least in the Prasad-Sommerfield limit. An SU(3) model with two stages of symmetry breaking, via two different chains, designed to mimic the more complicated SO(10) grand unified theory, is also considered. The spectrum of monopoles has only been partially discussed. It is found the pure monopole solutions known can be be extended to the dyon case, in a similar way to how this was done in SO(3). The Bogomolny bound, important in the uniqueness discussion, had previously only been applied where the Higgs fields are in the adjoint representation. It is generalized here and used to establish uniqueness of the dyon solutions found. The SU(3) model contains a doubly charged monopole in the second stage of breaking, but only in one of the two symmetry breaking chains. The equations of motion that would describe how the monopole "disappears" as we pass from one chain to the other, have not been solved. The generalized Bogomolny bound procedure, introduced here, offers hope that a solution to this problem can be found.
- Pub Date:
- Physics: Elementary Particles and High Energy