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Title: Infinite-dimensional multiplets in particle physics
Author: Koller, Karl
Awarding Body: University of London
Current Institution: Imperial College London
Date of Award: 1969
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In the Reggeization procedure of higher symmetry groups, which has been proposed by Delbourgo, Rashid, Strathdee and Salam, particles are described by a trajectory in the complex Casimir plane of the most degenerate representations of these groups. After a short review of Reggeization of U(6) ⨂ U(6) as an example of this program in chapter I, some of the mathematical problems encountered in the Reggeization of higher symmetry groups are studied in chapter II and III. The degenerate representation functions for the groups SO(v), SU(v) and SU(v) ⨂ SU(v) together with their non-compact forms SO(v-1,1), SU(v-1,1) and SL(v,C) are shown to be Gegenbauer functions in chapter II. The representation functions of the second kind are derived and properties of Gegenbauer functions are given a group theoretic interpretation. The analytic reduction of trajectories of these groups with respect to any of their sub-groups is performed in chapter III, this is clone for functions of the first and second kind. Covariant propagators for the Reggeized SO(v) theory are written down for any v, these give the usual Reggeization results of the rotation group for v = 3 and the "Lorentz pole" hypothesis for v,= 4. A unified derivation of Lorentz group matrix elements in a SU(2), SU(1,1), and U(1)AT(2) basis is given in chapter IV for all continuous linear representations in reflexive Banach spaces. The transformation functions between different bases are also determined. The analytic continuation of the principal series to the complementary series and of infinite-dimentional representations to finite-dimensional representations is studied in detail. Following Feldman and Matthews infinite-dimensional fields of the Lorentz group are constructed. In chapter V Feynman rules for infinite-dimensional fields are written down and scattering amplitudes for pole diagrams are calculated.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available