The usage of normal coordinate methods for the nonlinear realization of symmetries

Frederic Donovan Liebrand, Purdue University

Abstract

In quantum field theory the spontaneous breakdown of a symmetry is accompanied by the appearance of a massless Goldstone particle corresponding to each broken generator of the symmetry group. If the original realization of that symmetry is non-linear, then the group transformations on the Goldstone fields take the form of general coordinate transformations, with the fields identified as coordinates on the group cost manifold. Using normal coordinate methods, the classical action as well as the perturbative expansion of the theory's quantum effects may then be obtained in a manifestly group invariant form. This thesis examines and develops these uses of normal coordinate methods and non-linear realizations. For the case in which an internal symmetry group is non-linearly realized by bosonic Goldstone fields, this formalism is already well-developed. We review this formalism, applying it to the non-linear limit of two models of the electroweak sector, the standard model and the model of Gelmini and Roncadelli (GR). In each case certain interactions occurring at SSC energies, namely those involving the longitudinal components of the vector gauge bosons, are found to be enhanced over those encountered in the linear limit. We discuss the physical meaning of the non-linear limit, and, working at the one-loop level, we evaluate the most significant interactions involving either fermions or the charged scalars of the GR model. The methodology used above is then extended to a case in which the symmetry is not purely internal--the non-linear realization of the $N$ = 1 supersymmetry due to Akulov and Volkov. We develop the geometry on the coset manifold, and then exploit it to perturbatively isolate the manifestly supersymmetric one-loop effects of the Akulov-Volkov model.

Degree

Ph.D.

Advisors

Clark, Purdue University.

Subject Area

Particle physics

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