The Hamiltonian formulation of General Relativity: myths and reality

A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in "Gravitation: An Introduction to Current Research" (1962) 227] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i-iii) have been shown to be incorrect in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric $g_{\mu\nu}$ to lapse and shift functions and the three-metric $g_{km}$, which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself.Comment: References are added and updated, Introduction is extended, Subsection 3.5 is added, 83 pages; corresponds to the published versio

The Hamiltonian of Einstein affine-metric formulation of General Relativity

It is shown that the Hamiltonian of the Einstein affine-metric (first order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters as is the case for the second order formulation. In the second order formulation of ADM gravity the need for such a redefinition is the result of the non-canonical change of variables [arXiv: 0809.0097]. For the first order formulation, the necessity of such a redefinition "to correspond to diffeomorphism invariance" (reported by Ghalati [arXiv: 0901.3344]) is just an artifact of using the Henneaux-Teitelboim-Zanelli ansatz [Nucl. Phys. B 332 (1990) 169], which is sensitive to the choice of linear combination of tertiary constraints. This ansatz cannot be used as an algorithm for finding a gauge invariance, which is a unique property of a physical system, and it should not be affected by different choices of linear combinations of non-primary first class constraints. The algorithm of Castellani [Ann. Phys. 143 (1982) 357] is free from such a deficiency and it leads directly to four-diffeomorphism invariance for first, as well as for second order Hamiltonian formulations of GR. The distinct role of primary first class constraints, the effect of considering different linear combinations of constraints, the canonical transformations of phase-space variables, and their interplay are discussed in some detail for Hamiltonians of the second and first order formulations of metric GR. The first order formulation of Einstein-Cartan theory, which is the classical background of Loop Quantum Gravity, is also discussed.Comment: 74 page

Neutrino Propagation in a Strongly Magnetized Medium

We derive general expressions at the one-loop level for the coefficients of the covariant structure of the neutrino self-energy in the presence of a constant magnetic field. The neutrino energy spectrum and index of refraction are obtained for neutral and charged media in the strong-field limit ($M_{W}\gg \sqrt{B}\gg m_{e},T,\mu ,| \mathbf{p}|$) using the lowest Landau level approximation. The results found within the lowest Landau level approximation are numerically validated, summing in all Landau levels, for strong $B\gg T^{2}$ and weakly-strong $B \gtrsim T^{2}$ fields. The neutrino energy in leading order of the Fermi coupling constant is expressed as the sum of three terms: a kinetic-energy term, a term of interaction between the magnetic field and an induced neutrino magnetic moment, and a rest-energy term. The leading radiative correction to the kinetic-energy term depends linearly on the magnetic field strength and is independent of the chemical potential. The other two terms are only present in a charged medium. For strong and weakly-strong fields, it is found that the field-dependent correction to the neutrino energy in a neutral medium is much larger than the thermal one. Possible applications to cosmology and astrophysics are considered.Comment: 23 pages, 4 figures. Corrected misprints in reference

Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.

BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362

The dynamics of grazed woodlands in southwest Queensland, Australia and their effect on greenhouse gas emissions

This study outlines the development of an approach to evaluate the sources, sinks, and magnitudes of greenhouse gas emissions from a grazed semiarid rangeland dominated by mulga (Acacia aneura) and how these emissions may be altered by changes in management. This paper describes the modification of an existing pasture production model (GRASP) to include a gas emission component and a dynamic tree growth and population model. An exploratory study was completed to investigate the likely impact of changes in burning practices and stock management on emissions. This study indicates that there is a fundamental conflict between maintaining agricultural productivity and reducing greenhouse gas emissions on a given unit of land. Greater agricultural productivity is allied with the system being an emissions source while production declines and the system becomes a net emissions sink as mulga density increases. Effective management for sheep production results in the system acting as a net source (∼60–200 kg CO2 equivalents/ha/year). The magnitude of the source depends on the management strategies used to maintain the productivity of the system and is largely determined by starting density and average density of the mulga over the simulation period. Prior to European settlement, it is believed that the mulga lands were burnt almost annually. Simulations indicate that such a management approach results in the system acting as a small net sink with an average net absorption of greenhouse gases of 14 kg CO2 equivalents/ha/year through minimal growth of mulga stands. In contrast, the suppression of fire and the introduction of grazing results in thickening of mulga stands and the system can act as a significant net sink absorbing an average of 1000 kg CO2 equivalents/ha/year. Although dense mulga will render the land largely useless for grazing, land in this region is relatively inexpensive and could possibly be developed as a cost-effective carbon offset for greenhouse gas emissions elsewhere. These results also provide support for the hypothesis that changes in land management, and particularly, suppression of fire is chiefly responsible for the observed increases in mulga density over the past century

Heave-ho! A laboratory model of an underfloor environment incorporating pyritiferous fill

Damage to domestic dwellings in the greater Dublin area of Ireland caused by the expansion of underfloor fill material containing pyrite has become a high-profile national problem in recent years. In this paper, a novel experiment is described in which the succession of underfloor materials, with vertical dimensions at full scale, is reproduced. The study has enabled the amount/rate of expansion and pressures generated due to the expansion of the pyritiferous fill, with and without imposed loading on the concrete slab, to be ascertained over a period of 800 days. The rates of expansion are relatively consistent with those recorded from reference pipe experiments. These data form an important frame of reference for anticipating the time at which damage might begin to manifest itself in domestic dwellings