Fermions, Skyrmions and the 3-sphere

2009/08/14 by Stephen W. Goatham, Stephen W Goatham, Steffen Krusch
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Angular momentum #Dirac equation #Dirac fermion #Fermion #Mathematical physics #Physics #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #Quantum electrodynamics #Quantum mechanics #Regularization (linguistics) #Skyrmion #Spin (aerodynamics) #Theoretical physics #hep-th

paper · pdf · doi:10.1088/1751-8113/43/3/035402

published as J.Phys.A43:035402,2010 · 19 pages, 2 figures

arxiv created 2009/08/14 · openalex publication_date 2009/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

This paper investigates a background charge one Skyrme field chirally coupled to light fermions on the 3-sphere. The Dirac equation for the system commutes with a generalized angular momentum or grand spin. It can be solved explicitly for a Skyrme configuration given by the hedgehog form. The energy spectrum and degeneracies are derived for all values of the grand spin. Solutions for non-zero grand spin are each characterized by a set of four polynomials. The paper also discusses the energy of the Dirac sea using zeta-function regularization.

Citations

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• Axially symmetric multi-baryon solutions and their quantization in the chiral quark soliton model
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• Fermions coupled to skyrmions onS3