Status Updates From Quantum Field Theory: A Mod...

Historically, anticommutators and antimatter were introduced by Dirac, who was troubled that his theory seemed riddle with negative energy states. Since physical systems prefer the state of lowest energy, there is a finite probability that all the electrons in nature would decay into these negative energy states, thereby creating a catastrophe.

All physical states in quantum field theory can be labeled according to the eigenvalue of these two Casimir operators (since the Casimir commutes with all generators of the algebra). However, the physical significance of this new Casimir operator is not immediately obvious. It cannot correspond to spin, since our intuitive notion of angular momentum, which we obtain from nonrelativistic quantum mechanics...

Gradually, a small industry developed around finding nonperturbative solutions to QCD that could explain the confinement of quarks. On one hand, physicists showed that two-dimensional 'toy models' could reproduce many of the features that were required of a quantum field theory of quarks, such as confinement and asymptiotic freedom.