Abstract
In renormalizable unified gauge theories of the weak and electromagnetic interactions, for a given gauge group we ask the following question: Which representations of the scalar Higgs particles can reproduce a vector-meson mass spectrum in which one vector meson, the photon, remains massless and all other vector mesons acquire mass? Given the Higgs representation, we then examine what restrictions are placed on the charge operator of the theory. The examples of SU(3) and SU(3) \ifmmode\times\else\texttimes\fi{} U(1) are worked out in detail. The possible Higgs representations for all the unexceptional classical Lie groups are given. For each such group, there are some low-dimensional representations for which no solution exists.
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