120819205
Subgroups of Lie groups and separation of variables
Separable systems of coordinates for the Helmholtz equation ΔdΨ =EΨ in pseudo‐Riemannian spaces of dimension d have previously been characterized algebraically in terms of sets of commuting second order symmetry operators for the operator Δd. They have also been characterized geometrically by the form that the metric ds2=gik(x)dxidxk can take. We complement these characterizations by a group theoretical one in which the second order operators are related to continuous and discrete subgroups of G, the symmetry group of Δd. For d=3 we study all separable coordinates that can be characterized in terms of the Lie algebra L of G and show that they are of eight types, seven of which are related to the subgroup structure of G. Our method clearly generalizes to the case d≳3. Although each separable system corresponds to a pair of commuting symmetry operators, there do exist pairs of commuting symmetries S1,S2 that are not associated with separable coordinates. For subgroup related operators we show in detail just...
17212560
Superintegrability on the two-dimensional hyperboloid. II
In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras.
120256112
CLEBSCH--GORDAN COEFFICIENTS AND SPECIAL FUNCTION IDENTITIES. II. THE ROTATION AND LORENTZ GROUPS IN 3-SPACE.
It is shown that the construction of concrete models of Clebsch‐Gordan decompositions for tensor products of irreducible group representations leads to a wide variety of special function identities. In this paper the representation theory of the rotation and Lorentz groups in 3‐space is used to give elegant derivations of identities involving Languerre, Gegenbauer, hypergeometric, and generalized hypergeometric functions. Some of these identities may be new in this general form.
120822220
Separation of variables in Einstein spaces. I. Two ignorable and one null coordinate
Computes and classifies all Einstein spaces and their corresponding coordinate systems such that the Hamilton-Jacobi equation admits a separation of variables with two ignorable and one essential null coordinates. The authors find that all such spaces correspond to plane-fronted gravitational waves of Petrov type N. They also give necessary conditions which a general space-time must have in order to admit coordinates of the type studied. Furthermore, the integrability conditions for Helmholtz (Schrodinger) separability are completely solved.
121892369
Lie theory and the wave equation in space–time. I. The Lorentz group
In this article we begin a study of the relationship between separation of variables and the conformal symmetry group of the wave equation ψtt −Δ3ψ=0 in space–time. In this first article we make a detailed study of separation of variables for the Laplace operator on the one and two sheeted hyperboloids in Minkowski space. We then restrict ourselves to homogeneous solutions of the wave equation and the Lorentz subgroup SO(3,1) of the conformal group SO(4,2). We study the various separable bases by using the methods of integral geometry as developed by Gel’fand and Graev. In most cases we give the spectral analysis for these bases, and a number of new bases are developed in detail. Many of the special function identities derived appear to be new. This preliminary study is of importance when we subsequently study models of the Hilbert space structure for solutions of the wave equation and the Klein–Gordon equation ψtt−Δ3ψ=λψ.
120152328
Lie theory and separation of variables. 11. The EPD equation
We show that the Euler–Poisson–Darboux equation {∂tt−∂rr−[(2m+1)/r]∂r}Θ=0 separates in exactly nine coordinate systems corresponding to nine orbits of symmetric second‐order operators in the enveloping algebra of SL(2,R), the symmetry group of this equation. We employ techniques developed in earlier papers from this series and use the representation theory of SL(2,R) to derive special function identities relating the separated solutions. We also show that the complex EPD equation separates in exactly five coordinate systems corresponding to five orbits of symmetric second‐order operators in the enveloping algebra of SL(2,C).
1159458
Study of quasielastic scattering using charged-current νμ -iron interactions in the MINOS near detector
Kinematic distributions from an inclusive sample of 1.41×10^6 charged-current ν_μ interactions on iron, obtained using the MINOS near detector exposed to a wide-band beam with peak flux at 3 GeV, are compared to a conventional treatment of neutrino scattering within a Fermi gas nucleus. Results are used to guide the selection of a subsample enriched in quasielastic ν_μFe interactions, containing an estimated 123,000 quasielastic events of incident energies 1<E_ν<8  GeV, with ⟨E_ν⟩=2.79  GeV. Four additional subsamples representing topological and kinematic sideband regions to quasielastic scattering are also selected for the purpose of evaluating backgrounds. Comparisons using subsample distributions in four-momentum transfer Q^2 show the Monte Carlo model to be inadequate at low Q^2. Its shortcomings are remedied via inclusion of a Q^2-dependent suppression function for baryon resonance production, developed from the data. A chi-square fit of the resulting Monte Carlo simulation to the shape of the Q^2 distribution for the quasielastic-enriched sample is carried out with the axial-vector mass M_A of the dipole axial-vector form factor of the neutron as a free parameter. The effective M_A which best describes the data is 1.23^(+0.13)_(−0.09)(fit)^(+0.12)_(−0.15)(syst)  GeV.
952390
Search for flavor-changing non-standard neutrino interactions by MINOS
We report new constraints on flavor-changing non-standard neutrino interactions from the MINOS experiment, in which neutrino versus antineutrino interactions can be distinguished on an event-by-event basis. We analyzed a combined set of beam neutrino and antineutrino data from the well-understood NuMI beam, and found no evidence for deviations from standard neutrino mixing. The observed energy spectra constrain the non-standard neutrino interactions parameter to the range −0.20
1036381
Measurement of neutrino oscillations with the MINOS detectors in the NuMI beam.
This Letter reports new results from the MINOS experiment based on a two-year exposure to muon neutrinos from the Fermilab NuMI beam. Our data are consistent with quantum-mechanical oscillations of neutrino flavor with mass splitting |Deltam2| = (2.43+/-0.13) x 10(-3) eV2 (68% C.L.) and mixing angle sin2(2theta) > 0.90 (90% C.L.). Our data disfavor two alternative explanations for the disappearance of neutrinos in flight: namely, neutrino decays into lighter particles and quantum decoherence of neutrinos, at the 3.7 and 5.7 standard-deviation levels, respectively.
119270975
The 2010 Interim Report of the Long-Baseline Neutrino Experiment Collaboration Physics Working Groups
In early 2010, the Long-Baseline Neutrino Experiment (LBNE) science collaboration initiated a study to investigate the physics potential of the experiment with a broad set of different beam, nearand far-detector configurations. Nine initial topics were identified as scientific areas that motivate construction of a long-baseline neutrino experiment with a very large far detector. We summarize the scientific justification for each topic and the estimated performance for a set of far detector reference configurations. We report also on a study of optimized beam parameters and the physics capability of proposed Near Detector configurations. This document was presented to the collaboration in fall 2010 and updated with minor modifications in early 2011. PACS numbers: 14.60.Lm, 14.60.Pq, 95.85.Ry, 13.15+g, 13.30.Ce, 11.30.Fs, 14.20.Dh, 26.65.+t, 25.30.Pt, 29.40.Ka, 29.40.Gx ∗ Corresponding author: bob.wilson@colostate.edu
110095326
The Cleo III silicon vertex detector
The CLEO collaboration has embarked on an ambitious upgrade of the CLEO detector to match the upgrade of the CESR accelerator to luminosities of 2 × 10 33 cm −2 sec −1 . This will bring a factor ten improvement in the measurement of rare B decays and hence, increased sensitivity to physics at high mass scales and also the possibility of measuring CP violation. The upgrade includes a new four layer double-sided silicon detector. Each double-sided silicon wafer is 2.6 cmx 5.1 cm × 300 μ m . To maximize solid angle coverage with minimal material in the detector volume the detector chains are very long, up to 5 detectors per electronic readout channel, resulting in large series resistance and large detector capacitance. Moderate backgrounds permit the electronics to operate with a 1–3 μ s shaping time. A new front-end low noise preamplifier is being developed to maximize the signal to noise ratio, along with a modified SVX chip used for analog to digital conversion and sparsification. The detectors are connected to the electronics hybrid by a thin double sided kapton flex circuit. The length of the detector chains also requires novel mechanical support structures — CVD diamond beams axe the baseline solution. We are currently near the end of the prototype stage for all aspects for the project and will move into production by late summer. The detector will be installed in early 1998.