INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS ELECTRIC CHARGE FORM FACTOR ACCORDING TO SL(6,C) INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS ELECTRIC CHARGE FORM FACTOR ACCORDING TO SL(6,C) *** On leave of absence from Atomic Energy Centre, Dacca, East Paki

ELECTRIC CHARGE FORM FACTOR ACCORDING TO SL(6,C) 1) Any meaningful relativistic generalization of SU(6) symmetry leads to non-compact groups and infinite multiplets, and hence to practical difficulties in carrying out detailed calculations. This accounts for the long interval that has elapsed, between the first proposal to study the group P*SL(6,C) (semi-direct product of the Poincare" group P with SL(6,C) and the first complete calculation presented in this report. Previously we have cal-2 culated the strong Yukawa vertex, but to lowest order in the momenta only. The weak and electromagnetic vertices are much simpler to evaluate, because only two infinite multiplets are involved. In fact, the calculation of all such vertices may be simply reduced to the calculation of a prototype. This latter, which may be tentatively identified with the charge form factor, is evaluated in this paper. The baryons are assigned to a unitary, irreducible representation roup (1) . As in prev ation whose tensorial basis is 2 3 4 of the group (1) . As in previous publications* * * we use the represent-9 with k = 3 and N = --. The exact form of the electromagnetic vertex is not yet known. However, except for the possible existence of correction terms with higher derivatives, the charge part of the interaction is related to the current where Q is the usual SU(6) charge operator. In momentum space this is where t = (p-p'f < 0 is the invariant momentum transfer. 2) The current (2) has a formal similarity with the Born approximation in local field theory, and we shall therefore refer to the approximation as the "local limit". This notion of locality is of course not the same as the locality of the conventional Dirac theory. The charge form factor G E (t) is defined by and Dirac locality means Ggft)} a 1 , whereas in our "local limit" The principal feature of weak and electromagnetic interactions In a relativistic SU(6) theory is thus the appearance of damping at the vertex, which makes it possible to set up a highly convergent perturbation theory. It turns out that this damping is essentially the same for all the states in the infinite multlplet, and hence for all values of the spin. The usual difficulties of higher spin theories, both of convergence and of positive definiteness, are completely absent. In The resulting values of G E (t) are also shown i