Complex angular momentum and three-dimensional Lorentz group

Decomposition of the Principal Series of Unitary Irreducible Representations of SU(2, 2) Restricted to the Subgroup SU(1,1)⊗SU(2)

“…1 Toller et ai. have demonstrated that such an expansion in the crossed channel provides a natural framework for the Regge pole model of high energy scattering phenomenology. [2][3][4] The strong forces between hadrons satisfy so-called internal symmetries in addition to the Poincare space-time symmetry. In particular, the charge inqependence of these strong forces is believed to be an exact symmetry expressed by the invariance of the scattering operator under the rotations of the isotopic spin group.…”

“…We propose that a possible way that remnants of broken symmetries which combine Poincare and internal symmetries are retained by the amplitude is that it continues to have an expansion in unitary representation functions of the little groups of the primordial symmetry group. In this work we shall attempt to find the remnants of a symmetry which combines the internal isotopic spin symmetry with Poincare symmetry; In accordance with the above hypothesis, we shall assume that the scattering amplitude can be expanded in representation functions of a new "little group" which we take to be SU (2,2).…”

“…The unitary irreducible representations of SU (2,2) are labeled by the eigenvalues of three Casimir operators. 5 -7 SU(2, 2) contains the direct product subgroup SU(1, 1) ® SU (2).…”

“…The unitary irreducible representations of SU (2,2) are labeled by the eigenvalues of three Casimir operators. 5 -7 SU(2, 2) contains the direct product subgroup SU(1, 1) ® SU (2). We obtain a Regge-like expansion with correlated isotopic spin by interpre-ting SU(1, 1) to be the fixed-t Poincare little group and SU (2) to be the isotopiC spin group.…”

“…5 -7 SU(2, 2) contains the direct product subgroup SU(1, 1) ® SU (2). We obtain a Regge-like expansion with correlated isotopic spin by interpre-ting SU(1, 1) to be the fixed-t Poincare little group and SU (2) to be the isotopiC spin group. Thus the transformations in SU(t, 1) ® SU (2) are physical space-time and internal symmetry transformations.…”