The convergenece difficulty of the self-force of the electron has been inherent in the classical theory, and it is essencically due to the assumption that the source of the field is a geometrical point. Recently, Bopp has proposed a new method to remove this difficully by taking the Lagrange-function which involves the higher space-time derivatives of the field quantities. For example, we would obtain the finite field energy, provided that the scalar potential φ satisfies the following equation in the presence of a point singularity resting at the origin,
Δ(Δ - x² ) ψ = - 4πδ (x^→)   (I)
Because ψ is given by the suitable linear combination of the Coulomb potential and Yukawa potential having the common source at the origin so as to be finite up to the singularity.
When Lagrange- function contains the second time- derivatives of the field quantities as in Bopp s case, the field equations are 4-th order with respect to the time differentiation. So we cannot use the ordinary method of field quantization. Nevertheless, we can show that the quantization of such a field is formally possible by the analogous method to the well-known Heisenberg-Pauli's one - what is an aim of this paper.
As a result of this quantization, it becomes clear that the field is made up of two kinds of Bose particles, one of which has the positive enegry but another the negative enegry. Therefore the total field enegry is never positive difinite. Moreover, the system cannot form any stable statc, when the interaction with the sigularity is introduced. This is the greatest diffculty of Bopp's Theory. But, the self-enegry of the total system still remains finite the quantized form of the theory as in the classical one. Of course, the zero-point enegry -which is a quantum effect - is present and its abosolute value is infinie.
Here we take the unitaristic standpoint of view as in original Bopp's theory. So, for example, we consider the coordinate of the singular point only as a simple parameter, and describe its motion by the classical equation derived from Born's principle, which is not of the canonical form. Therefore thr Hamilton-function of the field does not coincide with the total enegry of the system. Finally we pick up such a part of enegry that is only dependent upon the coodinates of the singularity and show that it takes the form of the enegry expression of a particle with a negative mass, when making a uniform motion with a small velocity.

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It was shown by several authors that the perturbation theory, which proved in the case of quantum electrodynamics to be so powerfull a method of attack, was not adequate for the problems concerning the interaction of mesons with nucleons, firstly because their interaction constant g^{2 /}hc is not small enough in contrast to l^2/hc which describes the interaction of electrons with electromagnetic field, and secondly the proper mesonic field around a nucleon is of dipole type having higher singularities as compared to the proper electromagnetic field around an electron. Thus the adequate method of approximation for the strong interaction between mesons and nucleons has been set forth by Wentzel, and for the case of moderate as well as strong coupling the ordinary atomic system, has been proposed by S. Tomonaga. By using the latter method, detailed investigations were done for charged longitudinal . symmetrical longitudinal and neutral pseudoscalar mesons interacting with- nucleons. In the present paper we will now investigate the problem about the interaction of nucleons with charged vector mesons, taking into account not only the longitudinal but also the transverse part in order to know the complete natures of the interaction. To simplify the problem, it is also here assumed as has been done by Wentzel and Tomonaga, that the nucleon is infinitely heavy. Then the interaction energies between vector mesons and nucleons are separated into two parts, the longitudinal and the transverse part and as to the latter part, it can be shown that only the transverse mesons, whose orbital angular moments are perpendicular to the spins, i. e. l = j which we call c-component of the mesons interact with nucleons.

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