DUAL CHARGES OF A SUBGROUP IN GAUGE THEORIES——MAGNETIC MONOPOLES OF SU₂ & SO₃ GAUGE FIELD

Abstract：

In this paper,we discuss magnetic monopo]es of an U1-subgroup in SU2 and SO3 broken gauge theories,on the basis of fibre-bundle theory.We derive a general ex- pression for the electromagnetic potentials around magnetic monopoles,which,accord- ing to the usual connection between the electromagnetic potentials and field-strength tensors,leads naturally to't Hooft's definition of the electromagnetic field-strength tensors.Furthermore,from the view-point of fibre-bundle theory,we elucidate some problems concerning which there exist different opinions in the present literature. Our conclusions are summarized as follows. 1)In general,the description of magnetic monopoles in SU2 and SO3 broken gauge theories needs,in addition to SU2 or SO3 gauge potentials,the introduction of an unimodular Higgs isovector field to specify the direction of charge in the isospin space. 2)For the existence of magnetic monopoles,it is only required that the corresponding principal SU2-or SO3-bundles be reduced to U1-or SO2-bundles,not that the corresponding SU2-or SO3-gauge potentials be also reduced to U1-or SO2-gauge potentials. 3)The usual conclusion that the values of magnetic monopoles depend only on the topological properties of the Higgs field holds for the product SU2-or SO3-bundle. For the nontrivial SO3-bundle a new detailed discussion is needed.