Monopoles in SU2-Yang-Mills Theory

Abstract

Static solutions of the SU2-Yang-Mills theory with given charge- and current sources have been studied for spherically symmetric situations. In addition to the well-known Coulomb-Biot-Savart solution we have found a large class of nonabelian solutions, which generalize the ones found previously [1] for purely electric sources. Here I shall concentrate on the situation without electric sources, which can be described as follws. The source currents are (in a particular gauge)

$${\rm j_a^0 = 0,\,gr_0^3 \,j_a^k = \varepsilon _{kal} \,}{\rm e}_l \rm m(x)\,,$$

where e_k = r^k/r, x = r/r₀ and r₀ is an arbitrary length scale. The potentials resp. fields read

$${\rm A_a^0 = 0,\,gA_a^k = \varepsilon _{kal}} \,{\rm e}_l ({1 - \rm a(x)})/\rm r,]$$

$${\text{E}}_{\text{a}}^{\text{k}}{\text{ = 0}},{\mkern 1mu} {\text{gB}}_{\text{a}}^{\text{k}}{\text{ = }}[{{\text{e}}_{\text{a}}}{{\text{e}}_{\text{k}}}({\text{1 - }}{{\text{a}}^{\text{2}}}){\text{ + }}({{\text{e}}_{\text{a}}}{{\text{e}}_{\text{k}}}{\text{ - }}{\delta _{{\text{ak}}}}){\text{xa}}\prime {\text{ /}}{{\text{r}}^{\text{2}}}.$$

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Seminar given at XX. Internationale Universitätswochen für Kernphysik, Schladming, Austria, February 17–26, 1981