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arXiv · hep-ph/0507254

Scaling of Dirac Fermions and the WKB approximation

J. W. Van Orden·Sabine Jeschonnek·John Tjon
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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.

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J. W. Van Orden, Sabine Jeschonnek, John Tjon. 2005-07-21. Scaling of Dirac Fermions and the WKB approximation. https://doi.org/10.1103/physrevd.72.054020

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