Topological charges in monopole theories
Field theories with a compact, simply connected gauge group G are studied with respect to topological invariants and related conservation of charges. The theories of root systems and differential forms are used to derive the topological invariants. Spontaneous symmetry breaking through Higgs fields provides a subgroup H of G which is shown to yield a p-tuple of integer topological invariants called Higgs charges. Invariant polynomials of the Lie algebra of G homogeneous of degree p provide topological invariants which are explicitly related to these Higgs charges. From the charge operator of the Higgs field, a subgroup U(1) is constructed which leads to quantized charge. The magnetic monopole charge is determined as a linear combination of Higgs charges. The theory is illustrated for \(G=SU(n)\).
scientific article; zbMATH DE number 3956066
scientific article