Elementary analysis of the special relativistic combination of velocities, Wigner rotation, and Thomas precession

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to suit higher level students. We then give a summary of useful results, and suggest further reading in this often obscure field.Comment: V1: 25 pages, 6 figures; V2: 22 pages, 5 figures. The revised version is shortened and the arguments streamlined. Minor changes in notation and figures. This version matches the published versio

Charm and Bottom Semileptonic Decays

We review the present status of theoretical attempts to calculate the semileptonic charm and bottom decays and then present a calculation of these decays in the light--front frame at the kinematic point $q^2=0$. This allows us to evaluate the form factors at the same value of $q^2$, even though the allowed kinematic ranges for charm and bottom decays are very different. Also, at this kinematic point the decay is given in terms of only one form factor $A_{0}(0)$. For the ratio of the decay rates given by the E653 collaboration we show that the determination of the ratio of the Cabibbo--Kobayashi--Maskawa (CKM) matrix elements is consistent with that obtained from the unitarity constraint. At present, though, the unitarity method still has greater accuracy. Since comparisons of the semileptonic decays into $\rho$ and either electrons or muons will be available soon from the E791 Fermilab experiment, we also look at the massive muon case. We show that for a range of $q^2$ the $SU(3)_F$ symmetry breaking is small even though the contributions of the various helicity amplitudes becomes more complicated. For $B$ decays, the decay $B \rightarrow K^{*} \ell \bar{\ell}$ at $q^2=0$ involves an extra form factor coming from the photon contribution and so is not amenable to the same kind of analysis, leaving only the decay $B \rightarrow K^{*}\nu \bar{\nu}$ as a possibility. As the mass of the decaying particle increases we note that the $SU(3)$ symmetry becomes badly broken at $q^2=0$.Comment: Latex, 19 pages, two figures are attached, a minor change in the manuscript related to thi

The Kerry Babies, criminology, and Reinhart Koselleck

The Kerry Babies case was a criminal investigation that followed the discovery of a dead infant on a beach in the southwest of Ireland in April 1984. Charges were laid and dismissed. A tribunal of inquiry into alleged police malpractice followed, and the case returned to the courts 35 years later. This paper takes a multidimensional approach to historical time, drawing on the works of German philosopher Reinhart Koselleck to analyse the case, its legacy, and its implications for criminological theory. A Koselleckian approach – drawing in particular on the role of anachronisms, the mobilisation of memory and the categories of experience and expectation – facilitates a novel perspective on child killing, unmarried motherhood, and policing in 20th-century Ireland

An Improved Treatment of Optics in the Lindquist-Wheeler Models

We consider the optical properties of Lindquist-Wheeler (LW) models of the Universe. These models consist of lattices constructed from regularly arranged discrete masses. They are akin to the Wigner-Seitz construction of solid state physics, and result in a dynamical description of the large-scale Universe in which the global expansion is given by a Friedmann-like equation. We show that if these models are constructed in a particular way then the redshifts of distant objects, as well as the dynamics of the global space-time, can be made to be in good agreement with the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations, at the level of <3% out to z~2. Angular diameter and luminosity distances, on the other hand, differ from those found in the corresponding FLRW models, while being consistent with the 'empty beam' approximation, together with the shearing effects due to the nearest masses. This can be compared with the large deviations found from the corresponding FLRW values obtained in a previous study that considered LW models constructed in a different way. We therefore advocate the improved LW models we consider here as useful constructions that appear to faithfully reproduce both the dynamical and observational properties of space-times containing discrete masses.Comment: 7 pages, 5 figure

Optical energies of AllnN epilayers

Optical energy gaps are measured for high-quality Al1−xInxN-on-GaN epilayers with a range of compositions around the lattice match point using photoluminescence and photoluminescence excitation spectroscopy. These data are combined with structural data to determine the compositional dependence of emission and absorption energies. The trend indicates a very large bowing parameter of 6 eV and differences with earlier reports are discussed. Very large Stokes' shifts of 0.4-0.8 eV are observed in the composition range 0.13<x<0.24, increasing approximately linearly with InN fraction despite the change of sign of the piezoelectric fiel

Linear and nonlinear magneto-optical diffraction from one-dimensional periodic structures

Nonlinear magneto-optical diffraction from periodically structured samples has been studied using magnetization-induced second harmonic generation (MSHG). Several orders of diffraction were clearly observable in MSHG, along with a strong dependence on the magnetization. Sizeable asymmetry between the MSHG signal measured in positive and negative diffraction peaks, especially visible in second order, are explained by Fresnel factors. It was found that first-order diffraction hysteresis loops differ from all others by showing an ''overshoot'' at magnetization reversal, both in MSHG and in the linear magneto-optical Kerr effect. Tentatively this behavior is explained as due to inhomogeneous reversal of the magnetization in the stripes

CP-violating Majorana phases, lepton-conserving processes and final state interactions

The CP-violating phases associated with Majorana neutrinos can give rise to CP-violating effects even in processes that conserve total Lepton number, such as \mu -> eee+, \mu + e -> e + e and others. After explaining the reasons that make this happen, we consider the calculation of the rates for the process of the form \ell_a + \ell_b -> \ell_a + \ell_c, and its conjugate \bar\ell_a + \bar\ell_b -> \bar\ell_a + \bar\ell_c, where \ell_a, \ell_b and \ell_c denote charged leptons of different flavors. In the context of the Standard Model with Majorana neutrinos, we show that the difference in the rates depends on such phases. Our calculations illustrate in detail the mechanics that operate behind the scene, and set the stage for carrying out the analogous, more complicated (as we explain), calculations for other processes such as \mu -> eee+ and its conjugate.Comment: Latex, axodraw, 24 page

B -> K^* gamma from D -> K^* l nu

The B -> K^* gamma branching fraction is predicted using heavy quark spin symmetry at large recoil to relate the tensor and (axial-)vector form factors, using heavy quark flavor symmetry to relate the B decay form factors to the measured D -> K^* l nu form form factors, and extrapolating the semileptonic B decay form factors to large recoil assuming nearest pole dominance. This prediction agrees with data surprisingly well, and we comment on its implications for the extraction of |Vub| from B -> rho l nu.Comment: 10 page