Ambiguities with the relativistic δ-function potential

In many cases of physical interest, the 6-function potential is a very convenient approximation to more structured, and more difficult, short-ranged potentials. In relativistic theories, its use is often mandated because only a mathematical point has a relativistically invariant shape. Nevertheless, we were surprised recently to find difficulties and ambiguities regarding its use. Problems appear even in the case of one -body point scatterers, although it is generally assumed that all problems and paradoxes concerning one-body potentials have been resolved since the beginning of relativistic quantum theory.