A comment on the two definitions of the electric polarizability of a bound system in relativistic quantum theory

In 1999, F.A.B. Coutinho, Y.Nogami and Lauro Tomio published a paper entitled “Two definitions of the electric polarizability of a bound system in relativistic quantum theory”. The authors of ref.(1), dicussed the possibility of two definitions of the relativistic electric polarizability and the difference between the two definitions. In addition, the authors relate their definitions to the electric polarizability as it appears in a limited selection of studies. The authors of ref.(1) made serious mistakes in their analyses and conclusion. In addition, they ignored very valuable references which are essential to the problem of relativistic electric polarizability. It is the purpose of this note to point out the essential mistakes of ref.(1) and to point to some of the references which are of fundamental value to studying high energy photon scattering and the relativistic electric polarizability. The two definitions of the relativistic electric polarizability in ref.(1) are α and αQM . α is introduced as the relativistic electric polarizability which is obtained in quantum field theory while αQM is introduced as the relativistic electric polarizability which is obtained in single-particle quantum mechanics. The authors of ref.(1) stress that when the vacuum background is included in the system, α is obtained while αQM is obtained when the vacuum background is not included in the system. The electric polarizabilities in ref.(1) are defined as: