122194846
Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates
We classify and study those coordinate systems which permit R separation of variables for the wave equation in four‐dimensional space–time and such that at least one of the variables corresponds to a one‐parameter symmetry group of the wave equation. We discuss over 100 such systems and relate them to orbits of triplets of commuting operators in the enveloping algebra of the conformal group SO(4,2).
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.
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).
122430224
Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials
As a continuation of Paper 6 we study the separable basis eigenfunctions and their relationships for the harmonic oscillator Hamiltonian in two space variables with special emphasis on products of Ince polynomials, the eigenfunctions obtained when one separates variables in elliptic coordinates. The overlaps connecting this basis to the polar and Cartesian coordinate bases are obtained by computing in a simpler Bargmann Hilbert space model of the problem. We also show that Ince polynomials are intimately connected with the representation theory of SU (2), the group responsible for the eigenvalue degeneracy of the oscillator Hamiltonian.
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.
119430316
Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)
We consider the ``missing label'' problem for basis vectors of SU(3) representations in a basis corresponding to the group reduction SU(3)⊃O(3)⊃O(2). We prove that only two independent O (3) scalars exist in the enveloping algebra of S U (3), in addition to the obvious ones, namely the angular momentum L2 and the two SU(3) Casimir operators C(2) and C(3). Any one of these two operators (of third and fourth order in the generators) can be added to C(2), C(3), L2, and L3 to form a complete set of commuting operators. The eigenvalues of the third and fourth order scalars X(3) and X(4) are calculated analytically or numerically for many cases of physical interest. The methods developed in this article can be used to resolve a missing label problem for any semisimple group G, when reduced to any semisimple subgroup H.
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.
5924748
Testing Lorentz invariance and CPT conservation with NuMI neutrinos in the MINOS near detector.
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).
125313335
NOvA: Proposal to build a 30 kiloton off-axis detector to study nu(mu) ---> nu(e) oscillations in the NuMI beamline
121594432
RESONANCES IN THE SCATTERING OF ELECTRONS FROM ATOMS.
118717401
Simultaneous observations of extensive air showers and underground muons at Soudan 2
We have built a small proportional tube air shower array on the surface above the Soudan 2 proton decay detector in Soudan, Minnesota, USA. This array, in coincidence with the underground detector, allows simultaneous surface and underground observations of high energy cosmic ray showers. These observations, still in their initial stages, may eventually be able to provide information about the composition of cosmic ray primaries in the knee'' region of the energy spectrum. 4 refs.