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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 13, Pages 2023-2030

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.


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