A. Zee

A theory of lepton number violation and neutrino Majorana masses

It is emphasized that the successful relation MW = MZ cos θW does not mean that we have determined the SU(2) x U(1) transformation property of the Higgs sector. A simple modification of the Higgs sector leads to a wealth of exotic lepton number violating processes such as νμe− → νeμ− and to neutrino Majorana masses.It is emphasized that the successful relation M W = M Z cos θ W does not mean that we have determined the SU(2) x U(1) transformation property of the Higgs sector. A simple modification of the Higgs sector leads to a wealth of exotic lepton number violating processes such as ν μ e − → ν e μ − and to neutrino Majorana masses.

Chiral Anomalies, Higher Dimensions, and Differential Geometry

We determine the abelian and non-abelian chiral anomalies in 2n-dimensional spacetime by a differential geometric method which enables us to obtain the anomalies without having to calculate Feynman diagrams, as has been done by Frampton and Kephart. The advantage of this method is that the construction automatically satisfies the Wess-Zumino consistency condition, a condition which has direct physical interpretation. We hope that our analysis sheds light on the mathematical structure associated with chiral anomalies. The mathematical analysis is self-contained and a brief review of differential forms and other mathematical tools is included.

Quantum numbers of Majorana neutrino masses

Assuming that the neutrinos have Majorana masses, we study the possibility of conserving various lepton numbers and the form of the resulting neutrino mass matrix. A model of lepton-number violation proposed some years ago is found to have interesting properties in this connection. Various phenomenological implications are noted.

Some simple mixing and mass matrices for neutrinos

Abstract We argue that the accumulated neutrino data, including recent results from KamLAND and K2K, point to a neutrino mixing matrix with (V11,V21,V31; V21,V22,V32; V 13 ,V 23 ,V 33 )=(−2/ 6 ,1/ 6 ,1/ 6 ; 1/ 3 ,1/ 3 ,1/ 3 ; 0,1/ 2 ,−1/ 2 ) . We propose some simple neutrino mass matrices which predict such a mixing matrix.

Statistical Mechanics of Anyons

Abstract We study the statistical mechanics of a two-dimensional gas of free anyons-particles which interpolate between Bose-Einstein and Fermi-Dirac character. Thermodynamic quantities are discussed in the low-density regime. In particular, the second virial coefficient is evaluated by two different methods and is found to exhibit a simple, periodic, but nonanalytic behavior as a function of the statistics determining parameter.

Charged Scalar Field and Quantum Number Violations

Abstract 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.

Obtaining the neutrino mixing matrix with the tetrahedral group

Abstract We discuss various “minimalist” schemes to derive the neutrino mixing matrix using the tetrahedral group A 4 .

Viscosity renormalization in the Brinkman equation

The Brinkman equation purports to describe low‐Reynolds‐number flow in porous media in situations where velocity gradients are non‐negligible. The equation involves modifying the usual Darcy law by the addition of a standard viscosity term whose coefficient is usually identified with the pure‐fluid viscosity. It is argued instead that the porous medium induces a renormalization of viscosity, which is calculated in the dilute limit and separately in a self‐consistent approximation. The effective Brinkman viscosity is found to decrease from the pore‐fluid value. The calculation fails at low porosity but agrees at least in part with experiment. In addition, the relationship between the Brinkman equation and the phenomenological boundary condition of Beavers and Joseph is discussed and it is pointed out that their experimental configuration provides a simple means of measuring viscosity renormalization.

Universality of the correlations between eigenvalues of large random matrices

Abstract The distribution of eigenvalues of random matrices appears in a number of physical situations, and it has been noticed that the resulting properties are universal, i.e. independent of specific details. Standard examples are provided by the universality of the conductance fluctuations from sample to sample in mesoscopic electronic systems, and by the spectrum of energy levels of a non-integrable classical hamiltonian (the so-called quantum chaos). The correlations between eigenvalues, measured on the appropriate scale, are described in all those cases by simple gaussian statistics. Similarly numerical experiments have revealed the universality of these correlations with respect to the probability measure of the random matrices. A simple renormalization group argument leads to a direct understanding of this universality; it is a consequence of the attractive nature of a gaussian fixed point. Detailed calculations of these correlations are given for a general probability distribution (in which the logarithm of the probability is the trace of a polynomial of the matrix); the universality is shown to follow from an explicit asymptotic form of the orthogonal polynomials with respect to a non-gaussian measure. In addition it is found that the connected correlations, when suitably smoothed, exhibit, even when the eigenvalues are not in the scaling region, a higher level of universality than the density of states.

Large scale physics of the quantum hall fluid

Abstract We discuss the large-scale physics of incompressible Hall fluids from the point of view of universality and symmetry. We show that, in the scaling limit, incompressible Hall fluids are described by certain topological Chern-Simons gauge theories. The gauge field strengths are dual to conserved currents of the fluid. The Chern-Simons gauge theories unambiguously predict current algebras of chiral edge currents. We describe incompressible Hall fluids exhibiting edge currents which form a non-abelian Kac-Moody current algebra at level 1. Some new incompressible Hall fluids are described. Our analysis is derived from very general physical principles and should therefore lead to reliable results.