RESONANCES IN THE SCATTERING OF ELECTRONS FROM ATOMS.

title: The MINOS scintillator calorimeter system
abstract: The MINOS detectors will use extruded plastic scintillator strips, which are readout by wavelength-shifting fibres coupled to multi-pixel photodetectors. This technique provides excellent energy and spatial resolution. The MINOS detectors are described in detail along with results from the light output tests.

title: Testing Lorentz invariance and CPT conservation with NuMI neutrinos in the MINOS near detector.
abstract: A search for a sidereal modulation in the MINOS near detector neutrino data was performed. If present, this signature could be a consequence of Lorentz and CPT violation as predicted by the effective field theory called the standard-model extension. No evidence for a sidereal signal in the data set was found, implying that there is no significant change in neutrino propagation that depends on the direction of the neutrino beam in a sun-centered inertial frame. Upper limits on the magnitudes of the Lorentz and CPT violating terms in the standard-model extension lie between 10(-4) and 10(-2) of the maximum expected, assuming a suppression of these signatures by a factor of 10(-17).

title: Search for flavor-changing non-standard neutrino interactions by MINOS
abstract: 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

title: Search for magnetic monopoles with the Soudan 2 detector.
abstract: A search for grand unified theory magnetic monopoles making highly ionizing tracks in argon gas has been conducted using the Soudan 2 nucleon decay detector. This underground detector is a large fine-grained tracking calorimeter comprised of long drift tubes read out by proportional wires. No monopole candidates were observed in data taken over almost three years, yielding an upper flux limit of 8.7{times}10{sup {minus}15} cm{sup {minus}2}s{sup {minus}1}sr{sup {minus}1} for monopole velocities of .

title: Ultrahigh energy cosmic ray composition from surface air shower and underground muon measurements at Soudan 2.
abstract: The Soudan 2 experiment has performed time-coincident cosmic ray air shower and underground muon measurements. Comparisons to Monte Carlo predictions show that such measurements can make statistically significant tests of the primary composition in the knee region of the cosmic ray spectrum. The results do not support any significant increase in the average primary mass with energy in the range of {similar_to}10{sup 4} TeV per nucleus. Some systematic uncertainties remain, however, particularly in the Monte Carlo modeling of the cosmic ray shower.

title: Lie theory and the wave equation in space–time. I. The Lorentz group
abstract: 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.

title: Subgroups of Lie groups and separation of variables
abstract: 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...

title: Lie theory and separation of variables. 4. The groups SO(2,1) and SO(3)
abstract: Winternitz and coworkers have shown that the eigenfunction equation for the Laplacian on the hyperboloid x02−x12−x22=1 separates in nine orthogonal coordinate systems, associated with nine symmetric quadratic operators L in the enveloping algebra of SO (2,1). Corresponding to each of the operators L, we employ the standard one‐variable model for the principal series of representations of SO (2,1) and compute explicitly an L basis for the Hilbert space as well as the unitary transformations relating different bases. We also compute the associated results for realizations of these representations on the hyperboloid. Three of our bases are related to well‐known subgroup reductions of SO (2,1). Of the remaining six, one is related to Bessel functions, two to Legendre functions, and three to Lame functions. We show that there is virtually a perfect correspondence between the known theory of the Lame functions and the representation theory of SO (2,1) and SO (3).

title: Lie theory and the wave equation in space-time. 4. The Klein-Gordon equation and the Poincaré group
abstract: A detailed classification is made of all orthogonal coordinate systems for which the Klein–Gordon equation in space–time, ψtt−Δ3ψ=λψ, admits a separation of variables. We show that the Klein–Gordon equation is separable in 261 orthogonal coordinate systems. In each case the coordinate systems presented are characterized in terms of three symmetric second order commuting operators in the enveloping algebra of the Poincare group. This paper also consitutes an important step in the study of separation of variables for the wave equation in space–time ψtt−Δ3ψ=0, and its relation to the underlying conformal symmetry group O(4,2) of this equation.

title: Lie theory and separation of variables. 11. The EPD equation
abstract: 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).