부산대학교 도서관

In the analysis of scattering phenomena, one encounters dispersion relations of the form $F(x)=f(x)+\lim_{\varepsilon\rightarrow+0}\pi^{-1}\int_1^\infty[\text{Im}\,F(x')]\ [x'-x-i\varepsilon]^{-1}\,dx'$. The present paper is a mathematical survey of the properties of the solutions of this equation for $F(x)$. For elastic scattering, $\text{Im}\,F(x)=\exp[-i\delta(x)]\sin\delta(x)F(x)$, where $\delta$ is real-valued. For this case the author describes and compares the solutions given by M. Gourdin and A. Martin [Nuovo Cimento {\bf 8} (1958), no. 5, 699--707; RŽMat {\bf 1960} \#6613] and by R. Omnès [ibid. {\bf 8} (1958), 316--326; MR0094169 (20 \#688)] and discusses the possibility of using subtracted integrals in this approach. For inelastic scattering, the simple use of elastic unitarity and a complex phase shift $\delta$ leads to inconsistencies. The author then describes a satisfactory solution based on the use of complete unitarity, given in a recent paper by T. N. Pham and T. N. Truong [Phys. Rev. D {\bf 14} (1976), 185--188].