STRONG COULOMB COUPLING IN THE TODOROV EQUATION

A positronium-like system with strong Coulomb coupling, considered in its pseudoscalar sector, is studied in the framework of relativistic q uantum constraint dynamics with the Todorov choice for the potential. Case's method of self-adjoint extension of singular potentials, which avoids explicit introduction of regularization cut-offs, is adopted. I t is found that, as the coupling constant alpha increases, the bound s tate spectrum undergoes an abrupt change at the critical value alpha = alpha(c) = 1/2. For alpha > alpha(c), the mass spectrum displays, in addition to the existing states for alpha < alpha(c), a new set of an infinite number of bound states concentrated in a narrow band starting at mass W = 0; all the states have indefinitely oscillating wave func tions near the origin. In the limit alpha --> alpha(c) from above, the oscillations disappear and the narrow band of low-lying states shrink s to a single massless state with a mass gap with the rest of the spec trum. This state has the required properties to represent a Goldstone boson and to signal spontaneous breakdown of chiral symmetry.