Non-Abelian monopoles break color. I. Classical mechanics

Monopoles which are sources of non-Abelian magnetic flux are predicted by many models of grand unification. It has been argued elsewhere that a generic transformation of the ''unbroken'' symmetry group H cannot be globally implemented on such monopoles for reasons of topology. In this paper, we show that similar topological obstructions are encountered in the mechanics of a test particle in the field of these monopoles and that the transformations of H cannot all be globally implemented as canonical transformations. For the SU(5) model, if H is SU(3)/sub C/ x U(1)/sub em/, a consequence is that color multiplets are not globally defined, while if H is SU(3)/sub C/ x SU(2)/sub WS/ x U(1)/sub Y/, the same is the case for both color and electroweak multiplets. There are, however, several subgroups K/sub T/, K/sub T/',. . . of H which can be globally implemented, with the transformation laws of the observables differing from group to group in a novel way. For H = SU(3)/sub C/ x U(1)/sub em/, a choice for K/sub T/ is SU(2)/sub C/ x U(1)/sub em/, while for H = SU(3)/sub C/ x SU(2)/sub WS/ x U (1)/sub Y/, a choice is SU(2)/sub C/ x U(1) x U(1) x U(1). The paper also develops the differential geometry of monopoles in a form convenient for computations