2005/10/31 by G. Sardanashvily · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Gauge group #Gauge theory #Geometry #Higgs boson #Higgs field #Higgs mechanism #Mathematics #Particle physics #Physics #Principal bundle #Spontaneous symmetry breaking #Symmetry breaking #Theoretical physics #Vector bundle
paper · pdf · doi:10.1142/s0219887806001065
openalex publication_date 2006/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In gauge theory, Higgs fields are responsible for spontaneous symmetry breaking. In classical gauge theory on a principal bundle P, a symmetry breaking is defined as the reduction of a structure group of this principal bundle to a subgroup H of exact symmetries. This reduction takes place if and only if there exists a global section of the quotient bundle P/H. It is a classical Higgs field. A metric gravitational field exemplifies such a Higgs field. We summarize the basic facts on the reduction in principal bundles and geometry of Higgs fields. Our goal is the particular covariant differential in the presence of a Higgs field.