The S-matrix is a fundamental object in making theoretical predictions for collider scattering experiments. It is inspired by a well-defined operator in non-relativistic quantum mechanics,
but is plagued with both ultraviolet (UV) and infrared (IR) divergences in quantum field theory. While UV divergences are now understood through the program of renormalization,
IR divergences remain an active area of research. In this talk, we explore three solutions to the IR divergence problem: i) The cross section method, ii) modification of the S-matrix, and iii) the coherent state formalism.
We will show how our modified S-matrix in theories with massless particles can be interpreted as remainder functions in N=4 super Yang-Mills theory, or as Wilson coefficients in Soft-collinear effective theory.
Examining its analytic structure thus provides a new probe to properties of familiar objects from scattering calculations.
