Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 048, 19 pages      arXiv:0805.4725      https://doi.org/10.3842/SIGMA.2008.048
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Solvable Two-Body Dirac Equation as a Potential Model of Light Mesons

Askold Duviryak
Institute for Condensed Matter Physics of National Academy of Sciences of Ukraine, 1 Svientsitskii Str., UA-79011 Lviv, Ukraine

Received October 29, 2007, in final form May 07, 2008; Published online May 30, 2008

Abstract
The two-body Dirac equation with general local potential is reduced to the pair of ordinary second-order differential equations for radial components of a wave function. The class of linear + Coulomb potentials with complicated spin-angular structure is found, for which the equation is exactly solvable. On this ground a relativistic potential model of light mesons is constructed and the mass spectrum is calculated. It is compared with experimental data.

Key words: two body Dirac equation; Dirac oscillator; solvable model; Regge trajectories.

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