Bootstrap mechanisms and unitary symmetries

Abstract

We study the consequences of the applications of the 'Bootstrap’ hypothesis to the Unitary Symmetries. The groups SU(3), SU (6), U(6,6) and their applications to the strong Interactions of the Hadrons are discussed in the first Chapter. In the second Chapter, we discuss some of the methods that have been used in the past in dynamical (bootstrap) calculations. In the third Chapter, we consider the P-wave quark-pseudoscalar meson Octet scattering and investigate whether the existence of the three quarks, Q, which belong to the spinor representation of SU(3) and are supposed to have fractional charges, can be explained in a self-consistent scheme. The calculation shows that there exists a reciprocal bootstrap relationship between quarks, Q and some other particles, which have the baxyon number 1/3, spin 3/2 and belong to the 15-dimensional representation of SU(3), Using the determinantal method the self-consistent values we have obtained are: NA 2429Mev.,5251 Mev., 22 and 32, where MQ, MQ and g22 are respectively the masses and couplings of Q and Q*. In the fourth Chapter, we consider the meson-baryon scattering in the context of U(6,6) symmetry and study the mass-splittings of the , baryon Octet and Decouplet by N/D method. It is assumed that the SU(3) symmetry is approximately exact so that the masses of the baxyon Octet and Decouplet obtained by using the U(6,6) vertices in the calculation should correspond roughly to their respective 80(3) degenerate masses. Although the results are very much cut off-dependent, the calculations shows that by varying the cut off, S and U(6,6) coupling, g parameters It is possible to obtain the mass-spilttings in the right direction. Considering the very much involved nature of the calculations, one may conclude that the results agree reasonably well with the known experimental facts.