As was emphasized by Feynman ... among others, the physics of superfluidity lies not in the presence of gapless excitations, but in the paucity of ga… - Anthony Zee

The goal of condensed matter physics is to understand the various states of matter. States of matter are characterized by the presence (or absence) of order: a ferromagnet becomes ordered below the transition temperature. In the Landau-Ginzburg theory ... , order is associated with spontaneous symmetry breaking, described naturally with group theory. Girvin and MacDonald first noted that the order in Hall fluids does not really fit into the Landau-Ginzburg scheme: We have not broken any obvious symmetry. The topological property of the Hall fluids provides a clue to what is going on. As explained in the preceding chapter, the ground state degeneracy of a Hall fluid depends on the topology of the manifold it lives on, a dependence group theory is incapable of accounting for. Wen has forcefully emphasized that the study of topological order, or more generally quantum order, may open up a vast new vista on the possible states of matter.

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.

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.