Conformal field theory has been a rich area of quantum field theory since its rise to prominence 50 years ago, contributing to statistical mechanics, condensed matter, string theory, and (of course) quantum mechanics.

In this talk, I will discuss some of the physical motivations behind the theory, and then delve into an introduction to its behavior in two dimensions.

I will introduce the Witt and Virasoro algebras, the conformal group, the operator product expansion, and normal ordering. I will also derive the two-point function from group symmetries (the “conformal bootstrap method”), and conclude with a short application to the free fermion/Ising model.