International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2005 / Article

Open Access

Volume 2005 |Article ID 976956 | https://doi.org/10.1155/IJMMS.2005.2023

Andrew Talmadge, "Symmetry breaking via internal geometry", International Journal of Mathematics and Mathematical Sciences, vol. 2005, Article ID 976956, 8 pages, 2005. https://doi.org/10.1155/IJMMS.2005.2023

Symmetry breaking via internal geometry

Received15 Nov 2004
Revised02 Jul 2005

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

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.


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