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It is shown that the conserved magnetic charge discovered by ’t Hooft in non−Abelian gauge theories with spontaneous symmetry breaking is not associated with the invariance of the action under a symmetry group. Rather, it is a topological characteristic of an isotriplet of Higgs fields in a three−dimensional space: the Brouwer degree of the mapping between a large sphere in configuration space and the unit sphere in field space provided by the normalized Higgs field ?a = φa (φbφb)−1/2. The use of topological methods in determining magnetic charge configurations is outlined. A peculiar interplay between Dirac strings and zeros of the Higgs field under gauge transformations is pointed out. The monopole−antimonopole system is studied.

Quantized vortices can occur around nodes of wavefunctions. This fact, discovered by Dirac (1931) but little noted since, is rederived here and examples are discussed. The derivation depends only on the wavefunction being single valued and continuous. Since the derivation does not depend upon the dynamical equations, the quantized vortices are expected to occur for many types of waves (i.e., electromagnetic, acoustic, etc.). Such vortices have appeared in the calculations (McCullough and Wyatt, Kuppermann) of the H + H2 molecular collisions and play a role in the chemical kinetics. In a companion paper, it is shown that quantized vortices occur when optical waves are internally reflected from the face of a prism or particle beams are reflected from potential energy barriers.

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