Two dimensional general covariance from three dimensions

A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of conserved charges that are associated with graphs in two dimensions and the Poisson algebra of the charges is closed. For 2-manifolds with boundary there are additional observables that have a Kac-Moody Poisson algebra. It is further shown that the theory is classically integrable and the general solution of the equations of motion is given. The quantum theory is described using Dirac quantization, and it is shown that there are quantum states associated with graphs in two dimensions.Comment: 10 pages (Latex), Alberta-Thy-19-9

Optical data processing using paraboloidal mirror segments

An optical data processing system using paraboloidal reflecting surfaces is disclosed. In the preferred embodiment the paraboloidal reflecting surfaces are segments of a paraboloidal mirror. A source of coherent light is in the focal plane of the first paraboloidal mirror segment which collimates the beam and reflects it toward a second paraboloidal mirror surface. The information to be analyzed, on a transparency for example, is placed in the collimated beam. The beam is reflected from the second paraboloidal mirror segment and focused on a Fourier transform plane. A photon detector could be placed in the Fourier transform plane or suitable spatial filters, with the filtered beam then being reflected from a third paraboloidal mirror segment to be focused on a reconstruction plane

A wearable headset for monitoring electromyography responses within spinal surgery

Purpose: This research examines an approach for enhancing the efficiency of spinal surgery utilising the technological capabilities and design functionalities of wearable headsets, in this case Google Glass. The aim was to improve the efficiency of the selective dorsal rhizotomy neurosurgical procedure initially through the use of Glass via an innovative approach to information design for an intraoperative monitoring display. Methods Utilising primary and secondary research methods the development of a new electromyography response display for a wearable headset was undertaken. Results: Testing proved that Glass was fit for purpose and that the new intraoperative monitor design provided an example platform for the innovative intraoperative monitoring display; however, alternative wearable headsets such as the Microsoft HoloLens could also be equally viable. Conclusion: The new display design combined with the appropriate wearable technology could greatly benefit the selective dorsal rhizotomy procedure

2+1 Gravity without dynamics

A three dimensional generally covariant theory is described that has a 2+1 canonical decomposition in which the Hamiltonian constraint, which generates the dynamics, is absent. Physical observables for the theory are described and the classical and quantum theories are compared with ordinary 2+1 gravity.Comment: 9 page

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

General covariance, and supersymmetry without supersymmetry

An unusual four-dimensional generally covariant and supersymmetric SU(2) gauge theory is described. The theory has propagating degrees of freedom, and is invariant under a local (left-handed) chiral supersymmetry, which is half the supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the theory reveals the remarkable feature that the local supersymmetry is a consequence of Yang-Mills symmetry, in a manner reminiscent of how general coordinate invariance in Chern-Simons theory is a consequence of Yang-Mills symmetry. It is possible to write down an infinite number of conserved currents, which strongly suggests that the theory is classically integrable. A possible scheme for non-perturbative quantization is outlined. This utilizes ideas that have been developed and applied recently to the problem of quantizing gravity.Comment: 17 pages, RevTeX, two minor errors correcte

Health and cancer prevention: knowledge and beliefs of children and young people

Objective: To collect information from children and young people about their knowledge of and attitudes towards cancer and their understanding of health and health related behaviours to inform future health promotion work. Design: Questionnaire survey of 15-16 year olds, and interviews with play materials with 9-10 year old children. Setting: Six inner city, suburban, and rural schools. Subjects: 226 children aged 15-16 years and 100 aged 9-10 years. Main outcome measures: Knowledge about different types of cancer; beliefs about health; sources of information; quality of research data obtainable from young children about cancer and health. Results: Both samples knew most about lung cancer, but there was also some knowledge of breast and skin cancer and leukaemia. Smoking, together with pollution and other environmental factors, were seen as the dominant causes of cancer. Environmental factors were mentioned more often by the inner city samples. Television and the media were the most important sources of information. Young people were more worried about unemployment than about ill health. More than half the young people did not describe their health as good, and most said they did not have a healthy lifestyle. Children were able to provide detailed information about their knowledge and understanding by using drawings as well as interviews. Conclusions: Children and young people possess considerable knowledge about cancer, especially about lung cancer and smoking, and show considerable awareness of predominant health education messages. Despite this knowledge, many lead less than healthy lifestyles. Health is not seen as the most important goal in life by many young people; the circumstances in which many children and young people live are not experienced as health promoting

Phase transition in quantum gravity

A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some approximation. We outline a quantum field theory calculation, based on general relativity as the classical theory, which implies a phase transition in quantum gravity. The order parameters are composite fields derived from spacetime metric functions. These are massless below a critical energy scale and become massive above it. There is a corresponding breaking of classical symmetry.Comment: 5 pages (Latex), 1 eps figure. For Proceedings of the 8th. Canadian Conference on General Relativity and Relativistic Astrophysic

On Singularity Resolution in Quantum Gravity

We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity programme, and is based on an alternative to the Schr\"odinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute "singularity resolution" in quantum gravity.Comment: 12 page