Symmetry breaking via internal geometry (Q2576003)

Summary: 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