Anthony Zee

“Rotations in 3-dimensional Euclidean space ... form the poster child of group theory and are almost indispensable in physics. Think of rotating a rigid object, such as a bust of Newton. After two rotations in succession, the bust, being rigid, has not been deformed in any way; it merely has a different orientation. Thus, the composition of two rotations is another rotation.”

“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 ...”

“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 fight for credit goes on in every field, but in theoretical physics, it is almost a way of life, since ideas are by nature ethereal. And the stakes are high: the victor gets to go to Stockholm, while the loser is consigned to the dustbin of history; a history largely written by the victor with the help of an army of idolaters and science writers.”

“... The quantum Hall system consists of a bunch of electrons moving in a plane in the presence of an external magnetic field B 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.”

“As was emphasized by Feynman ... among others, the physics of superfluidity lies not in the presence of gapless excitations, but in the paucity of gapless excitations. (After all, the Fermi liquid has a continuum of gapless modes.) There are too few modes that the superfluid can lose energy and momentum to.”

“It is almost an article of faith among theoretical physicists, enunciated forcefully by Einstein among others, that the fundamental laws should be orderly and simple, rather than arbitrarily and complicated.”

“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.”

“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?”

“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.”

“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 show that the introduction of a charged scalar particle into the standard theory leads to numerous phenomenological consequences. In particular, muon-neutrino scattering on electron can resonate in the s-channel, a fact which is potentially important in high-energy neutrino experiments and conceivably relevant in explaining the recently reported underground muon events from Cygnus X-3. We focus on the violation of various quantum numbers, including electron, muon, and tauon numbers.”