Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories

We study spacetime diffeomorphisms in Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.Comment: 12 pages, no figures; REVTeX; uses multicol,fancyheadings,eqsecnum; to appear in Phys. Rev.

How to design and evaluate interventions to improve outcomes for patients with multimorbidity

Multimorbidity is a major challenge for patients and healthcare providers. The limited evidence of the effectiveness of interventions for people with multimorbidity means that there is a need for much more research and trials of potential interventions. Here we present a consensus view from a group of international researchers working to improve care for people with multimorbidity to guide future studies of interventions. We suggest that there is a need for careful consideration of whom to include, how to target interventions that address specific problems and that do not add to treatment burden, and selecting outcomes that matter both to patients and the healthcare system. Innovative design of these interventions will be necessary as many will be introduced in service settings and it will be important to ensure methodological rigour, relevance to service delivery, and generalizability across healthcare systems

Evaluation of radiometric and geometric characteristics of LANDSAT-D imaging system

With vegetation masked and noise sources eliminated or minimized, different carbonate facies could be discriminated in a south Florida scene. Laboratory spectra of grab samples indicate that a 20% change in depth of the carbonate absorption band was detected despite the effects of atmospheric absorption. Both bright and dark hydrothermally altered volcanic rocks can be discriminated from their unaltered equivalents. A previously unrecognized altered area was identified on the basis of the TM images. The ability to map desert varnish in semi-arid terrains has economic significance as it defines areas that are less susceptible desert erosional process and suitable for construction development

Temporal and spatial dynamics of CO2 air-sea flux in the Gulf of Maine

Ocean surface layer carbon dioxide (CO2) data collected in the Gulf of Maine from 2004 to 2008 are presented. Monthly shipboard observations are combined with additional higher‐resolution CO2 observations to characterize CO2 fugacity ( fCO2) and CO2 flux over hourly to interannual time scales. Observed fCO2 andCO2 flux dynamics are dominated by a seasonal cycle, with a large spring influx of CO2 and a fall‐to‐winter efflux back to the atmosphere. The temporal results at inner, middle, and outer shelf locations are highly correlated, and observed spatial variability is generally small relative to the monthly to seasonal temporal changes. The averaged annual flux is in near balance and is a net source of carbon to the atmosphere over 5 years, with a value of +0.38 mol m−2 yr−1. However, moderate interannual variation is also observed, where years 2005 and 2007 represent cases of regional source (+0.71) and sink (−0.11) anomalies. We use moored daily CO2 measurements to quantify aliasing due to temporal undersampling, an important error budget term that is typically unresolved. The uncertainty of our derived annual flux measurement is ±0.26 mol m−2 yr−1 and is dominated by this aliasing term. Comparison of results to the neighboring Middle and South Atlantic Bight coastal shelf systems indicates that the Gulf of Maine exhibits a similar annual cycle and range of oceanic fCO2 magnitude but differs in the seasonal phase. It also differs by enhanced fCO2 controls by factors other than temperature‐driven solubility, including biological drawdown, fall‐to‐winter vertical mixing, and river runoff

Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space

Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms to be projectable to phase-space, for generally covariant theories. This main result throws new light on the old fact that the algebra of gauge generators in the phase space of General Relativity, or other generally covariant theories, only closes as a soft algebra and not a a Lie algebra. The deep relationship between these two issues is clarified. In particular, we see that the second one may be understood as a side effect of the procedure to solve the first. It is explicitly shown how the adoption of specific metric-dependent diffeomorphisms, as a way to achieve projectability, causes the algebra of gauge generators (constraints) in phase space not to be a Lie algebra --with structure constants-- but a soft algebra --with structure {\it functions}.Comment: 22 pages, version to be published in Classical & Quantum Gravit

Gravitational observables, intrinsic coordinates, and canonical maps

It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism transformations has remained obscure. In a symmetry-inspired approach we construct invariants out of canonically induced active gauge transformations. These invariants may be intepreted as the full set of dynamical variables evaluated in the intrinsic coordinate system. The functional invariants can explicitly be written as a Taylor expansion in the coordinates of any observer, and the coefficients have a physical and geometrical interpretation. Surprisingly, all invariants can be obtained as limits of a family of canonical transformations. This permits a short (again geometric) proof that all invariants, including the lapse and shift, satisfy Poisson brackets that are equal to the invariants of their corresponding Dirac brackets.Comment: 4 pages, to appear in Modern Physics Letters

Follow Up of Transiting Hot Jupiters with the OpenScience Observatories

We have been using the Open University OpenScience Observatories (OSO) to undertake follow up observations of known transiting hot Jupiters for the past three years. Here we present recent system characterisation and transit timing results for WASP-52b and HAT-P-23b and report on the performance of the observatory. The OSO consists of two 0.4 meter class telescopes (PIRATE and COAST) used for undergraduate distance learning and research (Kolb et al 2018). The telescopes, located at Teide Observatory on Tenerife at an altitude of 2390m, can be operated remotely in real time for teaching or fully autonomously via an automated scheduler. Teide Observatory provides an excellent location with typical seeing of 0.6” and an average 280 clear nights per year. Our new observations, supplemented with additional data from a telescope located in the UK and previously published results, show that HAT-P-23b is slightly less inflated than previously reported and not eccentric. We find that a linear ephemeris is the best fit to the available timing data. For WASP-52b we slightly prefer a quadratic ephemeris indicative of period change. Further observations through the 2020-21 observing season should discriminate between the linear and quadratic ephemerides