Introduction to scale invariant scattering and its application to 2D systems at criticality

We review some pertinent notions on S-matrix in (1+1)-dimensional quantum field theory and the 2-dimensional Euclidean field theory description of systems at criticality. From these ideas, we establish a connection between scattering amplitudes and critical properties via the scale invariant scattering formalism. We exploit this relation to tackle previously intractable problems at criticality. We then conclude by mentioning some exact results obtained by implementing the scale invariant scattering on disordered systems, systems with local symmetry, and systems with coupled symmetries.