| Abstract: | Let F be a SUN gauge field on the space-time manifold M4, bλ（x） （λ=0,1, 2, 3） the gauge potentials, the field strengths and Q（x） a Higgs field. All quantities b, fλμ and Q（x） are SUN'-valued, i.e. they are represented by N×N anti-hermitian traceless matrices.Let M4' be the set of x such that Q（x）≠0 and define on M4', where The following results are obtained:Theorem 1. The 1st set of Maxwell equations Fλμ,v+Fμv,λ+Fvλ,μ=0 are satisfied for arbitrary bλ if and only if with Here s is an integer, 1≤s≤N-1.Suppose the conditions in theorem 1 are satisfied.Theorem 2. If s is a space-like two-dimensional surface, the value of dual charges contained in s defined by is equal to lq', where l is an integer and Theorem 3. The value of dual charges contained in S is equal to the integral which is independent of the gauge potentials.Theorem 4. The least positive value q' of dual charge can be attained by some Higgs fields.Remarks（a） When N=2, the results obtained are consistent with those of t Hooft, Arafune and Hou etc.（b） For N=3, we give an answer to the question of quantized values of dual charges which was discussed by Marciano and Pagels.（c） The Higgs field ø（x） is a mapping from M'4 into the AⅢ type symmetric space SUN/S(Us X UN-s) and the integral is an extension of Kronecker index for N=2. |
