Causality Sum Rules in Conventional Scattering Matrices

A recent preprint on arXiv (2608.10427) introduces a technique for directly establishing causality sum rules within traditional scattering matrices, commonly utilized in photonic and electromagnetic applications. The researchers demonstrate that by eliminating the time advance from the reference domain and applying the earliest-arrival delay for each channel, one can create a domain-delayed matrix. This matrix maintains real-frequency passivity and reestablishes the causal time origin. With specific assumptions of analyticity, transparency, and regularity, it transforms into a Schur function, facilitating a Cayley-Herglotz construction. The derived projected and determinant constraints limit coherent channel superpositions and total multichannel loss, recovering Rozanov's absorber limit and extending to multichannel frameworks.