Analytic eigenenergies of the Dirac equation with finite degrees of freedom under a confining linear potential using basis functions localized in spacetime
Abstract
Considering the propagation of fields in the spacetime continuum and the welldefined features of fields with finite degrees of freedom, the wave function is expanded in terms of a finite set of basis functions localized in spacetime. This paper presents the analytic eigenenergies derived for a confined fundamental fermionantifermion pair under a linear potential obtained from the Wilson loop for the nonAbelian YangMills field. The Hamiltonian matrix of the Dirac equation is analytically diagonalized using basis functions localized in spacetime. The squared lowest eigenenergy (as a function of the relativistic quantum number when the rotational energy is large compared to the composite particle masses) is proportional to the string tension and the absolute value of the Dirac's relativistic quantum number related to the total angular momentum, consistent with the expectation.
 Publication:

arXiv eprints
 Pub Date:
 January 2015
 arXiv:
 arXiv:1501.04837
 Bibcode:
 2015arXiv150104837F
 Keywords:

 High Energy Physics  Theory
 EPrint:
 v1: 6 pages