Ah, group theory! The entire subject is amazing and amusing. Who would have expected that three Platonic solids—the cube, tetrahedron, and icosahedro… - 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.

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.

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.