On the Theories of Higher Derivative and Non-Local Couplings, II
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It is generally granted that in theories of non-local couplings, the field equations(in mechanics, the equations of motion)are the integro-differential equations containing in their interaction terms an arbitrary function, the so-called form factor, and in a previous paper of this series, discussions have been done on these(c-number)equations, assuming the validity of the perturbation theory. In this paper, the convergency of the perturbation method is investigated and then it is shown that among the general solutions of these integro-differential equations, we can construct some special solutions which tend to the solutions of free equations as the coupling constant approaches zero. It is, moreover, found that the motion specified by these special solutions conforms to the equations which are localized in the time-like direction and have as manifold solutiors as free equations. The similar arguments are also done on the theories of the higher derivative couplings whose formal solutions have been constructed extensively in the previous paper.
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