Quantum field theory (QFT) works remarkably well for making theoretical predictions in collider scattering experiments. One of the fundamental objects in these calculations, the scattering matrix (S-matrix), is inspired by a well defined operator in non-relativistic quantum mechanics, but is plagued with both ultraviolet (UV) and infrared (IR) divergences in QFT. The UV divergences are now understood through the program of renormalization, but IR divergences remain an active area of research. We have explored three approaches to ameliorate the problem of IR divergences, all of which will be discussed in this talk: i) The cross section method using the KLN theorem, ii) exploiting factorization to modify of the S-matrix in theories with massless particles, and iii) the coherent state formalism.
