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Title: Non-linear group actions in particle physics
Author: Isham, Christopher John
Awarding Body: University of London
Current Institution: Imperial College London
Date of Award: 1969
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We formulate precisely the concept of a non-linear realization using the mathematical structure of a G-manifold. The chiral SU(n) x SU(n) transformations of the pseudoscalar mesons, for any n, are constructed from these techniques and some SU3 O- octet scattering lengths are calculated from the resulting chiral invariant interaction Lagrangians. The formalism is then extended using the theory of fibre bundles to include nucleon multiplets. We then return to the mesons and show that the interaction Lagrangian can be expressed in terms of a certain metric tensor on the G-manifold. Using this approach the properties of the currents in the theory are investigated and the close connection between the non-linear theory and Sugawara's theory of currents is exhibited. We also indicate in this section how vector and axial-vector particles may be introduced into the scheme. The non-linear realization spaces are then embedded in Euclidean linear representation spaces and the theory that chiral symmetries may be regarded as linear ones in which the fields are constrained is developed. Finally in two appendices we discuss some of the basic properties of differential geometry and fibre bundle theory that are used in the main text.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available