2005/09/21 by Rabin Banerjee, Shinichi Deguchi · 1 citation
Mathematics · Physics and Astronomy · #BRST quantization #Black Holes and Theoretical Physics #Covariant transformation #Gauge boson #Gauge covariant derivative #Gauge fixing #Gauge theory #Geometry #Hamiltonian lattice gauge theory #High-Energy Particle Collisions Research #Hypersphere #Introduction to gauge theory #Mathematical physics #Mathematics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum gauge theory #Supersymmetric gauge theory #Yang–Mills theory #hep-th
paper · pdf · doi:10.1016/j.physletb.2005.10.067
published as Phys.Lett.B632:579-585,2006 · 15 pages, revtex4
arxiv created 2005/09/21 · openalex publication_date 2005/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A gauge-fixing procedure for the Yang–Mills theory on an n-dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler's condition, we apply the BRST gauge-fixing procedure to the Yang–Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang–Mills field and associated fields are derived in manifestly O(n+1) covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the n-dimensional flat space.