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Two-Body Dirac equations of constraint dynamics provide a covariant frameworkto investigate the problem of highly relativistic quarks in meson bound states.This formalism eliminates automatically the problems of relative time andenergy, leading to a covariant three dimensional formalism with the same numberof degrees of freedom as appears in the corresponding nonrelativistic problem.It provides bound state wave equations with the simplicity of thenonrelativistic Schroedinger equation. Unlike other three-dimensionaltruncations of the Bethe-Salpeter equation, this covariant formalism has beenthoroughly tested in nonperturbatives contexts in QED, QCD, and nucleon-nucleonscattering. Here we continue the important studies of this formalism byextending a method developed earlier for positronium decay into two photons totests on the sixteen component quarkonium wave function solutions obtained inmeson spectroscopy. We examine positronium decay and then the two-gammaquarkonium decays of eta_c, eta'_c, chi_0c, chi_2c, and pi-zero The results forthe pi-zero, although off the experimental rate by 13%, is much closer than theusual expectations from a potential model.Comment: 4 pages. Presented at Second Meeting of APS Topical Group on Hadron  Physics, Nashville, TN, Oct 22-24. Proceedings to be published by Journal of  Physics (UK), Conference Serie

Two Gamma Quarkonium and Positronium Decays with Two-Body Dirac Equations of Constraint Dynamics