Studies in dual models

Abstract

This thesis is concerned with Dual Resonance Models, and in particular with their algebraic structures. Chapter one is an introduction to the subject of dual models, in which the known models are surveyed, and their most important features are indicated. Chapter two deals with the calculation of the determinants and other functions of infinite dimensional matrices which arise in the calculation of fermion and off-shell dual amplitudes. After explaining how these functions arise, a group-theoretical method of calculating them is given, which is much simpler than previous methods. In Chapter three recent work on super symmetry and graded Lie algebras is reviewed, and its relevance to theoretical particle physics in general and dual models in particular is indicated. The algebras underlying the known dual models, including the recently suggested 0(N) algebras, are seen to be graded Lie algebras. In Chapter Four it is pointed out that the finite sub algebras of these (infinite) dual model algebras are simple graded Lie algebras. Representations of these sub algebras are constructed using the superfield formalism of supersynmetry. Some of these representations extend to representations of the infinite algebras, and in certain cases they can be used to construct Fock space realizations of the generators of these (graded) algebras. In Chapter five n-point amplitudes corresponding to the C(N) algebras are constructed using bilinear form which are invariant under their finite subalgebras (described in Chapter four). The 4-point amplitudes are investigated, and it is found that their mass-spectrum contains ghost states N > 2 and for N=2 except in two space-time dimensions,.