Causality and the Dispersion Relation: Logical Foundations

摘要: "Strict causality" is the assumption that no signal whatsoever can be transmitted over a space-like interval in space-time, or travel faster than velocity of light vacuo. In this paper rigorous proof given logical equivalence strict causality ("no output before input") and validity dispersion relation, e.g., relation expressing real part generalized scattering amplitude as an integral involving imaginary part. This applies to general linear system with time-independent connection between freely variable input has advantage previous work tacit assumptions are made about analytic behavior single-valuedness amplitude, but, on contrary, shown imply upper half complex frequency plane. The relations first parts then terms phase shift.