We show that the introduction of a charged scalar particle into the standard theory leads to numerous phenomenological consequences. In particular, m… - Anthony Zee

Normally, the entropy of a system is extensive, that is, proportional to its volume. Somehow, a black hole has an entropy proportional to its surface rather than to its volume. This fact has led to the so-called holographic principle. Many fundamental physicists believe that this mysterious property of black holes holds the key to quantum gravity.

... 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> perpendicular to the plane. The magnetic field is assumed to be sufficiently strong so that the electrons all have spin up, say, so they may be treated as spinless fermions. As is well known, this seemingly innocuous and simple physical situation contains a wealth of physics, the elucidation of which has led to two Nobel prizes.

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.