On the Connection of the Scattering and Derivative Matrices with Causality

The connection between the S matrix and causality suggested by Kronig is analyzed, and it is found that the condition of causality implies that the poles of the analytical functions $S(k)$ are either on the imaginary axis or in the lower half-plane. The possibility of a close connection between the properties of the derivative R matrix and causality is also analyzed. Although all the properties of the R matrix could not be deduced from the requirements of causality, it is considered as an encouraging preliminary result that: (1) The referred distribution of the poles of $S(k)$ can be obtained from the properties of the R matrix. (2) These properties of the corresponding R matrix are unchanged under a transformation S(k)→e^ikλS(k), with λ positive, which preserves the causal nature of the theory.