Coherent states and the quantization of 1+1-dimensional Yang-Mills theory

This paper discusses the canonical quantization of 1+1-dimensional Yang-Mills theory on a spacetime cylinder, from the point of view of coherent states, or equivalently, the Segal-Bargmann transform. Before gauge symmetry is imposed, the coherent states are simply ordinary coherent states labeled by points in an infinite-dimensional linear phase space. Gauge symmetry is imposed by projecting the original coherent states onto the gauge-invariant subspace, using a suitable regularization procedure. We obtain in this way a new family of "reduced" coherent states labeled by points in the reduced phase space, which in this case is simply the cotangent bundle of the structure group K. The main result explained here, obtained originally in a joint work of the author with B. Driver, is this: The reduced coherent states are precisely those associated to the generalized Segal-Bargmann transform for K, as introduced by the author from a different point of view. This result agrees with that of K. Wren, who uses a different method of implementing the gauge symmetry. The coherent states also provide a rigorous way of making sense out of the quantum Hamiltonian for the unreduced system. Various related issues are discussed, including the complex structure on the reduced phase space and the question of whether quantization commutes with reduction

Keeping your eye on the rail: gaze behaviour of horse riders approaching a jump

The gaze behaviour of riders during their approach to a jump was investigated using a mobile eye tracking device (ASL Mobile Eye). The timing, frequency and duration of fixations on the jump and the percentage of time when their point of gaze (POG) was located elsewhere were assessed. Fixations were identified when the POG remained on the jump for 100 ms or longer. The jumping skill of experienced but non-elite riders (n=10) was assessed by means of a questionnaire. Their gaze behaviour was recorded as they completed a course of three identical jumps five times. The speed and timing of the approach was calculated. Gaze behaviour throughout the overall approach and during the last five strides before take-off was assessed following frame-by-frame analyses. Differences in relation to both round and jump number were found. Significantly longer was spent fixated on the jump during round 2, both during the overall approach and during the last five strides (p , 0.05). Jump 1 was fixated on significantly earlier and more frequently than jump 2 or 3 (p , 0.05). Significantly more errors were made with jump 3 than with jump 1 (p=0.01) but there was no difference in errors made between rounds

The acid production of bacillus welchii

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A 10B-based neutron detector with stacked Multiwire Proportional Counters and macrostructured cathodes

We present the results of the measurements of the detection efficiency for a 4.7 \r{A} neutron beam incident upon a detector incorporating a stack of up to five MultiWire Proportional Counters (MWPC) with Boron-coated cathodes. The cathodes were made of Aluminum and had a surface exhibiting millimeter-deep V-shaped grooves of 45{\deg}, upon which the thin Boron film was deposited by DC magnetron sputtering. The incident neutrons interacting with the converter layer deposited on the sidewalls of the grooves have a higher capture probability, owing to the larger effective absorption film thickness. This leads to a higher overall detection efficiency for the grooved cathode when compared to a cathode with a flat surface. Both the experimental results and the predictions of the GEANT4 model suggests that a 5-counter detector stack with coated grooved cathodes has the same efficiency as a 7-counter stack with flat cathodes. The reduction in the number of counters in the stack without altering the detection efficiency will prove highly beneficial for large-area position-sensitive detectors for neutron scattering applications, for which the cost-effective manufacturing of the detector and associated readout electronics is an important objective. The proposed detector concept could be a technological option for one of the new chopper spectrometers and other instruments planned to be built at the future European Spallation Source in Sweden. These results with macrostructured cathodes generally apply not just to MWPCs but to other gaseous detectors as well.Comment: 14 pages, 9 figure

On the uncertainty relations and squeezed states for the quantum mechanics on a circle

The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in the context of the uncertainty relations.Comment: 4 figure

Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

Feat or futile: Students' perceptions of group work at a University of Technology in South Africa

The increase in student enrolment at tertiary institutions in South Africa over the past few years has necessitated the need for group work without sacrificing the standard and integrity of education. Research has shown that group work offers many advantages to both lecturers and students. Interactive attributes such as teamwork, co-operation skills, leadership qualities, communication skills and confidentiality developed during group work are highly sought-after skills by prospective employers. This quantitative study aimed to determine whether students are positively or negatively inclined towards group work, as well as other possible factors influencing group work at a university of technology (UoT) in South Africa. A structured, close-ended questionnaire was administered to 309 students enrolled for the Applied Communication Skills course. The data were analysed using statistical methods. The results revealed that listening skills and mutual respect were crucial to develop good interpersonal skills needed for effective group work. When working in groups, students tend towards collectivism and negative aspects of group work, such as social loafing, are often overseen to maintain harmony and avoid direct confrontation with other individuals in the group. It was also found that male students agreed more strongly with negative conflict resolution than female students. Overall, the study showed that despite several negative aspects, students tended to be positively inclined towards group work

Gravitational radiation from nonaxisymmetric spherical Couette flow in a neutron star

The gravitational wave signal generated by global, nonaxisymmetric shear flows in a neutron star is calculated numerically by integrating the incompressible Navier--Stokes equation in a spherical, differentially rotating shell. At Reynolds numbers \Rey \gsim 3 \times 10^{3}, the laminar Stokes flow is unstable and helical, oscillating Taylor--G\"ortler vortices develop. The gravitational wave strain generated by the resulting kinetic-energy fluctuations is computed in both $+$ and $\times$ polarizations as a function of time. It is found that the signal-to-noise ratio for a coherent, $10^{8}$-{\rm s} integration with LIGO II scales as $6.5 (\Omega_*/10^{4} {\rm rad} {\rm s}^{-1})^{7/2}$ for a star at 1 {\rm kpc} with angular velocity $\Omega_*$. This should be regarded as a lower limit: it excludes pressure fluctuations, herringbone flows, Stuart vortices, and fully developed turbulence (for \Rey \gsim 10^{6}).Comment: (1) School of Physics, University of Melbourne, Parkville, VIC 3010, Australia. (2) Departamento de Fisica, Escuela de Ciencias,Universidad de Oriente, Cumana, Venezuela, (3) Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia. Accepted for publication in The Astrophysical Journal Letter

Equivalence of operator-splitting schemes for the integration of the Langevin equation

We investigate the equivalence of different operator-splitting schemes for the integration of the Langevin equation. We consider a specific problem, so called the directed percolation process, which can be extended to a wider class of problems. We first give a compact mathematical description of the operator-splitting method and introduce two typical splitting schemes that will be useful in numerical studies. We show that the two schemes are essentially equivalent through the map that turns out to be an automorphism. An associated equivalent class of operator-splitting integrations is also defined by generalizing the specified equivalence.Comment: 4 page