Scaling of Dirac Fermions and the WKB approximation

Abstract

We discuss a new method for obtaining the WKB approximation to the Dirac equation with a scalar potential and a time-like vector potential. We use the WKB solutions to investigate the scaling behavior of a confining model for quark-hadron duality. In this model, a light quark is bound to a heavy di-quark by a linear scalar potential. Absorption of virtual photons promotes the quark to bound states. The analog of the parton model for this case is for a virtual photon to eject the bound, ground-state quark directly into free continuum states. We compare the scaling limits of the response functions for these two transitions.

References in corpus (19)

• Generalized Parton Distributions
• Neutrino-pasta scattering: the opacity of nonuniform neutron-rich matter
• Quark-hadron duality in electron scattering
• The Q^2-Dependence of Nuclear Transparency for Exclusive ${\rho }^0$ Production
• Symmetry breaking and quark-hadron duality in structure functions
• Parton-Hadron Duality in Unpolarised and Polarised Structure Functions
• Locality of quark-hadron duality and deviations from quark counting rules above resonance region
• Local Duality and Charge Symmetry Violation in Quark Distributions
• Modeling quark-hadron duality for relativistic, confined fermions
• Operator Product Expansion and Quark-Hadron Duality: Facts and Riddles
• Electromagnetic response of confined Dirac particles
• Pion photoproduction on the nucleon
• Virtual photon asymmetry for confined, interacting Dirac particles with spin symmetry
• Effect of bound nucleon internal structure change on nuclear structure functions
• Quark-Hadron Duality and Scaling in Reduced QCD
• Modeling quark-hadron duality in polarization observables
• Restricted locality of quark-hadron duality in exclusive meson photoproduction reactions above the resonance region
• Spacelike and timelike response of confined relativistic particles
• Spin asymmetries for confined Dirac particles

Cited by in corpus (3)

• Regge trajectories of Excited Baryons, quark-diquark models and quark-hadron duality
• Exact relativistic Green's functions for the time-independent potentials
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description