STRONG COULOMB COUPLING IN THE TODOROV EQUATION

Abstract

A positronium-like system with strong Coulomb coupling, considered in its pseudoscalar sector, is studied in the framework of relativistic quantum 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. It is found that, as the coupling constant α increases, the bound state spectrum undergoes an abrupt change at the critical value α=αc=1/2. For α>αc, the mass spectrum displays, in addition to the existing states for α<αc, 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 functions near the origin. In the limit α→αc from above, the oscillations disappear and the narrow band of low-lying states shrinks to a single massless state with a mass gap with the rest of the spectrum. This state has the required properties to represent a Goldstone boson and to signal spontaneous breakdown of chiral symmetry.