The typical situation of a scattering process that we deal in the subsequent is that corresponding to short-range interactions. Therefore, in the asymptotic past and future the initial and final states of particles, respectively, behave as free ones.

1. 1.

   For\(P_j\ge P_i\) this is clear because then\(\log P_j/P_i\ge 1\). In the range\(P_j\in [0,P_i]\) the difference\(P_j \log (P_j/P_i)-P_j+P_i\) is\(\ge 0\), because it has a negative derivative with respect to\(P_j\) and it is zero at\(P_j=P_i\) (it is\(P_i\) for\(P_j=0\)).

Authors and Affiliations

1. Departamento de Física, Universidad de Murcia, Murcia, Spain

   José Antonio Oller

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Correspondence toJosé Antonio Oller.

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