Canonical Transformations and Path Integral Measures

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are discussed and used to show that the quantum mechanical version of the classical transformation does not leave the measure of the path integral invariant, instead inducing an anomaly. The relation to operator techniques and ordering problems is discussed, and special attention is paid to incorporation of the initial and final states of the transition element into the boundary conditions of the problem. Classical canonical transformations are developed to render an arbitrary power potential cyclic. The resulting Hamiltonian is analyzed as a quantum system to show its relation to known quantum mechanical results. A perturbative argument is used to suppress ordering related terms in the transformed Hamiltonian in the event that the classical canonical transformation leads to a nonquadratic cyclic Hamiltonian. The associated anomalies are analyzed to yield general methods to evaluate the path integral's prefactor for such systems. The methods are applied to several systems, including linear and quadratic potentials, the velocity-dependent potential, and the time-dependent harmonic oscillator.Comment: 28 pages, LaTe

Finding a moral homeground: appropriately critical religious education and transmission of spiritual values

Values-inspired issues remain an important part of the British school curriculum. Avoiding moral relativism while fostering enthusiasm for spiritual values and applying them to non-curricular learning such as school ethos or children's home lives are challenges where spiritual, moral, social and cultural (SMSC) development might benefit from leadership by critical religious education (RE). Whether the school's model of spirituality is that of an individual spiritual tradition (schools of a particular religious character) or universal pluralistic religiosity (schools of plural religious character), the pedagogy of RE thought capable of leading SMSC development would be the dialogical approach with examples of successful implementation described by Gates, Ipgrave and Skeie. Marton's phenomenography, is thought to provide a valuable framework to allow the teacher to be appropriately critical in the transmission of spiritual values in schools of a particular religious character as evidenced by Hella's work in Lutheran schools

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review

Genetic Risk Can Be Decreased: Quitting Smoking Decreases and Delays Lung Cancer for Smokers With High and Low CHRNA5 Risk Genotypes - A Meta-analysis.

BACKGROUND: Recent meta-analyses show that individuals with high risk variants in CHRNA5 on chromosome 15q25 are likely to develop lung cancer earlier than those with low-risk genotypes. The same high-risk genetic variants also predict nicotine dependence and delayed smoking cessation. It is unclear whether smoking cessation confers the same benefits in terms of lung cancer risk reduction for those who possess CHRNA5 risk variants versus those who do not. METHODS: Meta-analyses examined the association between smoking cessation and lung cancer risk in 15 studies of individuals with European ancestry who possessed varying rs16969968 genotypes (N=12,690 ever smokers, including 6988 cases of lung cancer and 5702 controls) in the International Lung Cancer Consortium. RESULTS: Smoking cessation (former vs. current smokers) was associated with a lower likelihood of lung cancer (OR=0.48, 95%CI=0.30-0.75, p=0.0015). Among lung cancer patients, smoking cessation was associated with a 7-year delay in median age of lung cancer diagnosis (HR=0.68, 95%CI=0.61-0.77, p=4.9∗10(-10)). The CHRNA5 rs16969968 risk genotype (AA) was associated with increased risk and earlier diagnosis for lung cancer, but the beneficial effects of smoking cessation were very similar in those with and without the risk genotype. CONCLUSION: We demonstrate that quitting smoking is highly beneficial in reducing lung cancer risks for smokers regardless of their CHRNA5 rs16969968 genetic risk status. Smokers with high-risk CHRNA5 genotypes, on average, can largely eliminate their elevated genetic risk for lung cancer by quitting smoking- cutting their risk of lung cancer in half and delaying its onset by 7years for those who develop it. These results: 1) underscore the potential value of smoking cessation for all smokers, 2) suggest that CHRNA5 rs16969968 genotype affects lung cancer diagnosis through its effects on smoking, and 3) have potential value for framing preventive interventions for those who smoke

De novo mutations in MED13, a component of the Mediator complex, are associated with a novel neurodevelopmental disorder

Genetics of disease, diagnosis and treatmen

A Population of Gamma-Ray Millisecond Pulsars Seen with the Fermi Large Area Telescope

Gamma-Ray Pulsar Bonanza Most of the pulsars we know about were detected through their radio emission; a few are known to pulse gamma rays but were first detected at other wavelengths (see the Perspective by Halpern ). Using the Fermi Gamma-Ray Space Telescope, Abdo et al. (p. 840 , published online 2 July; see the cover) report the detection of 16 previously unknown pulsars based on their gamma-ray emission alone. Thirteen of these coincide with previously unidentified gamma-ray sources, solving the 30-year-old mystery of their identities. Pulsars are fast-rotating neutron stars. With time they slow down and cease to radiate; however, if they are in a binary system, they can have their spin rates increased by mass transfer from their companion stars, starting a new life as millisecond pulsars. In another study, Abdo et al. (p. 845 ) report the detection of gamma-ray emission from the globular cluster 47 Tucanae, which is coming from an ensemble of millisecond pulsars in the cluster's core. The data imply that there are up to 60 millisecond pulsars in 47 Tucanae, twice as many as predicted by radio observations. In a further companion study, Abdo et al. (p. 848 , published online 2 July) searched Fermi Large Area Telescope data for pulsations from all known millisecond pulsars outside of stellar clusters, finding gamma-ray pulsations for eight of them. Their properties resemble those of other gamma-ray pulsars, suggesting that they share the same basic emission mechanism. Indeed, both sets of pulsars favor emission models in which the gamma rays are produced in the outer magnetosphere of the neutron star