... The quantum Hall system consists of a bunch of electrons moving in a plane in the presence of an external magnetic field <math>B</math> perpendic… - Anthony Zee

We discuss the problem of adding random matrices, which enable us to study Hamiltonians consisting of a deterministic term plus a random term. Using a diagrammatic approach and introducing the concept of "gluon connectedness," we calculate the density of energy levels for a wide class of probability distributions governing the random term, thus generalizing a result obtained recently by Brézin, Hikami, and Zee. The method used here may be applied to a broad class of problems involving random matrices.

Ah, group theory! The entire subject is amazing and amusing. Who would have expected that three Platonic solids—the cube, tetrahedron, and icosahedron—would pop up in constructing the Dynkin diagrams of the exceptional Lie algebras? Or that finite group theory could determine the remainder when 10¹⁰ is divided by 11?

Although group theory is certainly relevant for nineteenth-century physics, it really started to play an important role with the work of Lorentz and Poincaré, and became essential with quantum mechanics. Heisenberg opened up an entirely new world with his vision of an internal symmetry, the exploration of which continues to this day in one form or another. Beginning in the 1950s, group theory has come to play a central role in several areas of physics, perhaps none more so than in what I call fundamental physics ...