Interaction theory in a new isobaric spin space

Abstract

Utiyama's theory of interactions is extended to an isobaric spin space invariant under the group R 3 ∗ of three-dimensional complex rotations. Utiyama's formalism rests on the utilisation of certain simple invariance groups of the Lagrangian, which turn out to be R 2 and R 3 (two-dimensional and three-dimensional real rotation groups). These groups are found to be determined by the invariance properties of the Hilbert space built out of the representations of R 3 ∗ , in which we have defined our basic “elementary” fields. The group R 2 is associated with charge conversion, while R 3 yields the conservation of isobaric spin and strangeness. The conservation of baryon number is automatically given by the special form of the baryon fields. The group R 2 introduces the electromagnetic field; R 3 introduces “complexes” of pion-fields and one justifies the ΔI = 1 2 selection rule. The theory shows moreover that one can only have strangeness singlets which eliminate all fields belonging to the D(0, 1), D(1, 1 2 ) and D( 1 2 , 1) representations of R 3 ∗ which have not been observed experimentally. We can also explain the difference between Σ 0 and Λ 0 in our new space.