Abstract
An embedding of SU(2) and an internal symmetry group G into a larger group G̃ containing SU(2) and G as subgroups is constructed for all G possessing a generalized spin-½ quark model. The starting point is a set of three mathematical conditions for the embedding group G̃ which are derived from physically plausible assumptions. By group theoretical techniques due to Dynkin and Malcev, it is shown that the embedding group is already uniquely determined by the proposed conditions, with only one set of groups G for which two solutions are obtained. The results for G̃ are given explicitly. Identifying SU(2) as covering of the rotation group the spin extension G̃ is enlarged to an embedding G̃h of the homogeneous Lorentz group Lh and G. It is shown that Ḡh can also be obtained without using the spin extension. The minimal translation group which can be attached to Ḡh is calculated. The results are also taken over to the Budini-Fronsdal identification of SU(2).
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