R. Delbourgo

The covariant theory of strong interaction symmetries

A classification of particles is suggested based on a Ũ(12) symmetry scheme. This is a relativistic generalization of the U(6) symmetry. The spin 12 and 32 baryons are each described by 20-component spinors which satisfy Bargmann-Wigner equations and belong to the 3̲6̲4̲ representation of the Ũ(12) group while the vector and p. s. mesons belong to the representation 1̲4̲3̲. The procedure for writing fully relativistic form factors is worked out in detail for baryon-meson and meson-meson cases. The new results are the following: (1) FC(q2)FM(q2)∝1+q2<2μ>m, Where Fc and FM are (Sachs) electromagnetic form factors. (2) μD = 1 + 2m/< μ >, where < μ > is the mean mass of the 1- multiplet and m the nucleon mass. (3) μρ,K* = 3. The conventional U(6) results can be recovered by projecting to the positive energy subspace in the rest system for each particle. To any irreducible representation of the U(6) there corresponds one irreducible representation of Ũ(12) and vice versa.

ON THE DYNAMICAL ORIGIN OF SU(6)

Abstract We consider a relativistic dynamical model for massive quark-antiquark binding which gives rise to the rest symmetry U(6) ⊗ O(3) for the meson bound states.

Relativistic Extension of Non-Compact Symmetry Groups

The problem of relativistieally boosting the unitary representations of a non-compact spin-containing rest-symmetry group is solved by starting with non-unitary infinite-dimensional representations of a relativistic extension of this group, by adjoining to this extension four space-time translations and by the napplying Bargmann-Wigner equations to guarantee aunitary norm. The procedure has similarities to the conventional method of induced representations. The boosting problem considered here is the first step towards the solution of the problem of coupling of such infinite-dimensional representations which is also briefly investigated. Startin g from a rest-symmetry like U(6,6) a chain of subgroups GL(6), U(3,3), etc., is exhibited for collinear and coplanar processes, etc.

S - matrix elements in the two-particle unitarity approximation for a world of one space dimension

SummaryFor a world having a single spatial dimension we apply the unitarity equations in the two-particle approximation to deduce thecrossing-symmetric scattering amplitude and thereby determine the form factor and propagator of the theory ; comparison of the full amplitude with the « Born approximation » reveals their quite different asymptotic characters. The solution is also used to discuss the problem of overlapping final-state interactions and it is proved that the enhancement ismultiplicative in form.RiassuntoAd un mondo con una sola dimensione spaziale, si applicano le equazioni di unitarietà nell’approssimazione a due particelle per dedurre l’ampiezza di scattering nella simmetria incrociata e quindi determinare il fattore di forma e il propagatore della teoria; un confronto fra l’ampiezza intera e la « approssimazione di Born » mostra la grande diversità del loro comportamento asintotico. Ci si serve inoltre della soluzione per discutere il problema delle interazioni fra gli stati finali sovrapponentisi e si prova che il rafforzamento è di tipo moltiplicativo.

Green's functions for Regge trajectories

Abstract A Feynman-like calculus is sketched were Regge trajectories are associated with propagators belonging to infinite-dimensional representations of SL(2,C). It is suggested that such a phenomenological scheme may prove more convergent than normal perturbation theory.