Interior-boundary conditions for the Dirac equation at point sources in three dimensions

A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The works well in non-relativistic case, i.e., Laplacian operator. Here, we study how can be applied to Dirac operators. While this has successfully been done already one space dimension, and more generally codimension-1 boundaries, situation point sources three dimensions corresponds a codimension-3 boundary. One would expect that, such boundary, operators do not allow boundary because they are known interactions 3D, which also correspond condition. Indeed, confirm expectation here by proving that there no self-adjoint operator (truncated) Fock an IBC at configurations origin. However, present positive result showing (on consisting origin) away from those configurations, given plus sufficiently strong Coulomb potential.