Structure of Internal-Symmetry Groups

It is shown that, given SU(2) and $T$ invariance, their outer automorphisms, which must themselves be symmetries, form a one-parameter gauge group. Thus, from isospin conservation and time-reversal invariance, one gets hypercharge conservation. Similarly, from angular momentum conservation and $T$ invariance, one has fermion-number conservation. Further, the well-known empirical relations ${\mathrm{}(-1\mathrm{})\mathrm{}}^Y={\mathrm{}(-1\mathrm{})\mathrm{}}^{2I}$ and ${\mathrm{}(-1\mathrm{})\mathrm{}}^F={\mathrm{}(-1\mathrm{})\mathrm{}}^{2J}$ are derived.