Angular momentum magnetic monopoles and gauge theories

When an exact gauge symmetry group H is embedded in a larger group G which is broken back to H spontaneously, there are situations in which the angular momentum operator acquires a new term, t, where t1,t2,t3 generate an angular momentum sub-algebra of G. Thus internal and external symmetries are coupled. It is shown that the radial component of t is a linear combination of the generators of H. When H consists of a colour group and an electromagnetic U(1) generated by the electric charge operator Q which is a colour singlet, then the coefficient of Q in this decomposition is minus the magnetic charge occurring in the situation. For general H the structure of the decomposition of the radial component of t into generators of H completely determines the topological quantum numbers of the solution considered. The result provides a useful new tool for the model building of monopoles. (Auth.)