International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 13, Pages 2023-2030
doi:10.1155/IJMMS.2005.2023
Symmetry breaking via internal geometry
Department of Curriculum and Instruction, College of Education and Human Development, University of New Orleans, New Orleans 70148, LA, USA
Received 15 November 2004; Revised 2 July 2005
Copyright © 2005 Andrew Talmadge. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Gauge theories commonly employ complex vector-valued fields to
reduce symmetry groups through the Higgs mechanism of
spontaneous symmetry breaking. The geometry of the internal space
V is tacitly assumed to be the metric geometry of some static,
nondynamical hermitian metric k. In this paper, we consider
G-principal bundle gauge theories, where G is a subgroup of
U(V,k) (the unitary transformations on the internal vector space
V with hermitian metric k) and we consider allowing the
hermitian metric on the internal space V to become an additional
dynamical element of the theory. We find a mechanism for
interpreting the Higgs scalar field as a feature of the geometry
of the internal space while retaining the successful aspects of
the Higgs mechanism and spontaneous symmetry breaking