1996/09/25 by Mikhail S. Volkov, Volkov, Mikhail S.
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Einstein #Electroweak interaction #FOS: Physical sciences #Gauge (firearms) #Gauge group #Gauge theory #High Energy Physics - Theory (hep-th) #Mathematical physics #Parity (physics) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum electrodynamics #Quantum mechanics #Sphaleron #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9609201
19 pp, LaTeX, epsf, 2 postscript figures, Published in "Geometry and Integrable Models", Eds. P.N. Pyatov \& S.N.Solodukhin, World Scientific 1996, pp. 55-77
arxiv created 1996/09/25 · openalex publication_date 1996/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The dynamics of small perturbations around sphaleron and black hole solutions in the Einstein-Yang-Mills theory for the gauge group SU(2) is investigated. The perturbations can be split into the two independent sectors in accordance with their parity; each sector contains negative modes. The even-parity negative modes are shown to correspond to the negative second variations of the height of the potential energy barrier near the sphaleron. For the odd-parity sector, the existence of precisely n (the number of nodes of the sphaleron solution gauge field function) negative modes is rigorously proven. The same results hold for the Einstein-Yang-Mills black holes as well.