Relation of Isotopic Spin Space to Space-Time

The customary form of physical space as the direct product of space-time and isotopic spin space can be replaced by a certain fusion of these two spaces into one space if one widens the group from the Lorentz group to the conformal space-time group which endows particles with an intrinsic finite size. It is shown that the familiar space-time transformations continue to induce their familiar Dirac spinor transformations, while the new space-time transformations in general induce isotopic spin transformations as well. The detailed correspondence is worked out for a theory of $T=1\mathrm{}$ bosons coupled to $T=\frac{1}{2}$ fermions.