On the use of the imaginary-mass representations of the Poincaré group in scattering amplitudes

Spin Physics and the Theory of Strong Interactions

“…(By convenience, however, the word "spin" can be used also in such cases.) It has been shown by Hadjioannou [13] and Joos [14] that the Regge formalism in the crossed channel can indeed be interpreted in terms of the representations of the Poincaré group with negative mass squared.…”

“…The one-particle state of vacuum is described by a statistical operator of the form (13). An element g of the invariance group G transforms the operator (13) into the operator…”

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.…”

On the geometrical interpretation of the harmonic analysis of the scattering amplitude

“…In the last decade, many authors [1][2][3][4][5] contributed in making clear the role played in particle physics by the harmonic analysis of the scattering amplitude on the Poincare group. Consider the elastic scattering of two scalar particles of equal mass m and denote with T(s, t) the scattering amplitude, where 5 and t are the usual Mandelstam variables; i.e.…”

“…However one can also invert the situation and take t < 0 fixed and decompose the scattering amplitude in functions of s obtaining in this way the so-called ί-channel (or crossed-channel) phase-shift analysis. In the latter case, instead of the center of mass system the convenient system is the brick-wall system [4] and the little group is the non-compact group 50 (2,1). One of the great advantages of these decompositions is that the scattering amplitude is thereby separated into its dynamical part, contained in the partial-waves, and its symmetry part which is expressed through the various types of higher transcendental functions which appear in the representations.…”