2003/02/28 by H. Reinhardt, Hugo Reinhardt, T. Tok · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Dirac algebra #Dirac comb #Dirac equation #Dirac operator #Dirac spinor #Geometry #Hamiltonian (control theory) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Topological Materials and Phenomena #Torus #Vortex #Winding number #hep-th
paper · pdf · doi:10.1103/physrevd.68.065004
published as Phys.Rev. D68 (2003) 065004 · 19 pages, 11 figures, references added, minor corrections
arxiv created 2003/06/24 · openalex publication_date 2003/09/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The spectrum of the Dirac Hamiltonian in the background of crossing vortices is studied. To exploit the index theorem, and in analogy with the lattice, the space-time manifold is chosen to be the four-torus T4. For the sake of simplicity we consider two idealized cases: infinitely fat and thin transversally intersecting vortices. The time-dependent spectrum of the Dirac Hamiltonian is calculated and in particular the influence of the vortex crossing on the quark spectrum is investigated. For the infinitely fat intersecting vortices it is found that zero modes of the four-dimensional Dirac operator can be expressed in terms of those eigenspinors of the Euclidean time-dependent Dirac Hamiltonian which cross zero energy. For thin intersecting vortices the time gradient of the spectral flow of the Dirac Hamiltonian is steepest at the time at which the vortices cross each other.