Singular Potentials and the Z = 0 Condition
H. H. Aly, Harald J. W. Müller · Journal of Mathematical Physics · 1967
We consider an interaction Lagrangian consisting of renormalizable and nonrenormalizable terms. After a brief discussion of the vertex function and the boundary conditions determining the renormalization constant corresponding to a pseudoscalar bound state, we derive an explicit expression for the nonrelativistic S-matrix for scattering by the potential 1/r4. These results are then used to evaluate Z. The explicit expressions obtained contain a strong cut-off dependence which cannot be factorized out. However, a specific value of the cut-off reduces the equation to a well-known eigenvalue problem, so that in this case a discrete spectrum of bound states may be obtained.