Rotations in 3-dimensional Euclidean space ... form the poster child of group theory and are almost indispensable in physics. Think of rotating a rig… - Anthony Zee

That the exchange of a particle can produce a force was one of the most profound conceptual advances in physics. We now associate a particle with each of the known forces: for example, the photon with the electromagnetic force and the graviton with the gravitational force; the former is experimentally well established and while the latter has not yet been detected experimentally hardly anyone doubts its existence.

In the last few years, an interesting new subject, the study of topological quantum fluids, has emerged. Examples of topological quantum fluids include the Hall fluid, the chiral spin fluid, and the anyon superfluid.

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.