Theory of Neutrino Flavor Mixing

The depth of our theoretical understanding of neutrino flavor mixing should match the importance of this phenomenon as a herald of long-awaited empirical challenges to the standard model of particle physics. After reviewing the familiar, simplified quantum mechanical model and its flaws, I sketch the deeper understanding of both vacuum and matter-enhanced flavor mixing that is found in the framework of scattering theory. While the simplified model gives the ``correct answer'' for atmospheric, solar, and accelerator/reactor neutrino phenomena, I argue that a key insight from the deeper picture will simplify the treatment of neutrino transport in astrophysical environments---supernovae, for example---in which neutrinos play a dynamically important role.Comment: 18 pages. Written contribution to the proceedings of ``Frontiers of Contemporary Physics--II,'' held March 5-10, 2001 at Vanderbilt University, Nashville, Tennesse

Minkowski and Galilei/Newton Fluid Dynamics: A Geometric 3+1 Spacetime Perspective

A kinetic theory of classical particles serves as a unified basis for developing a geometric $3+1$ spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases on as common a footing as possible reveals that the particle four-momentum is better regarded as comprising momentum and \textit{inertia} rather than momentum and energy; and consequently, that the object now known as the stress-energy or energy-momentum tensor is more properly understood as a stress-\textit{inertia} or \textit{inertia}-momentum tensor. In dealing with both fiducial and comoving frames as fluid dynamics requires, tensor decompositions in terms of the four-velocities of observers associated with these frames render use of coordinate-free geometric notation not only fully viable, but conceptually simplifying. A particle number four-vector, three-momentum $(1,1)$ tensor, and kinetic energy four-vector characterize a simple fluid and satisfy balance equations involving spacetime divergences on both Minkowski and Galilei/Newton spacetimes. Reduced to a fully $3+1$ form, these equations yield the familiar conservative formulations of special relativistic and non-relativistic hydrodynamics as partial differential equations in inertial coordinates, and in geometric form will provide a useful conceptual bridge to arbitrary-Lagrange-Euler and general relativistic formulations.Comment: Belated upload of version accepted by MDPI Fluids. Additional material in the Introduction; added several tables and an additional appendi