Towards Loop Quantum Gravity without the time gauge

The Hamiltonian formulation of the Holst action is reviewed and it is provided a solution of second-class constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of Ashtekar-Barbero-Immirzi connections. This result emphasizes that the Loop Quantum Gravity quantization procedure can be applied when the time-gauge condition does not stand.Comment: 5 pages, accepted for publication in Phys. Rev. Let

Synchronous Quantum Gravity

The implications of restricting the covariance principle within a Gaussian gauge are developed both on a classical and a quantum level. Hence, we investigate the cosmological issues of the obtained Schr\"odinger Quantum Gravity with respect to the asymptotically early dynamics of a generic Universe. A dualism between time and the reference frame fixing is then inferred.Comment: 8 pages, Proceedings of the II Stueckelberg worksho

Shortcomings of the Big Bounce derivation in Loop Quantum Cosmology

We give a prescription to define in Loop Quantum Gravity the electric field operator related to the scale factor of an homogeneous and isotropic cosmological space-time. This procedure allows to link the fundamental theory with its cosmological implementation. In view of the conjugate relation existing between holonomies and fluxes, the edge length and the area of surfaces in the fiducial metric satisfy a duality condition. As a consequence, the area operator has a discrete spectrum also in Loop Quantum Cosmology. This feature makes the super-Hamiltonian regularization an open issue of the whole formulation.Comment: 4 pages, accepted for publication in Phys. Rev. D as a Rapid Communicatio

The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity

The implications of the SU(2) gauge fixing associated with the choice of invariant triads in Loop Quantum Cosmology are discussed for a Bianchi I model. In particular, via the analysis of Dirac brackets, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if paths are parallel to fiducial vectors only. This way the quantization procedure for the Bianchi I model is performed by applying the techniques developed in Loop Quantum Gravity but restricting the admissible paths. Furthermore, the local character retained by the reduced variables provides a relic diffeomorphisms constraint, whose imposition implies homogeneity on a quantum level. The resulting picture for the fundamental spatial manifold is that of a cubical knot with attached SU(2) irreducible representations. The discretization of geometric operators is outlined and a new perspective for the super-Hamiltonian regularization in Loop Quantum Cosmology is proposed.Comment: 6 page

Implications of the gauge-fixing in Loop Quantum Cosmology

The restriction to invariant connections in a Friedmann-Robertson-Walker space-time is discussed via the analysis of the Dirac brackets associated with the corresponding gauge fixing. This analysis allows us to establish the proper correspondence between reduced and un-reduced variables. In this respect, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if edges are parallel to simplicial vectors and the quantization of the model is performed via standard techniques by restricting admissible paths. Within this scheme, the discretization of the area spectrum is emphasized. Then, the role of the diffeomorphisms generator in reduced phase-space is investigated and it is clarified how it implements homogeneity on quantum states, which are defined over cubical knots. Finally, the perspectives for a consistent dynamical treatment are discussed.Comment: 7 pages, accepted for publication in Physical Review

More than range exposure: global otters’ vulnerability to climate change

Climate change impact on species is commonly assessed by predicting species’ range change, a measure of a species’ extrinsic exposure. However, this is only one dimension of species’ vulnerability to climate change. Spatial arrangement of suitable habitats (e.g., fragmentation), their degree of protection or human disturbance, as well as species’ intrinsic sensitivity, such as climatic tolerances, are often neglected. Here, we consider components of species’ intrinsic sensitivity to climate change (climatic niche specialization and marginality) together with components of extrinsic exposure (changes in range extent, fragmentation, coverage of protected areas, and human footprint) to develop an integrated vulnerability index to climate change for world’s freshwater otters. As top freshwater predators, otters are among the most vulnerable mammals, with most species being threatened by habitat loss and degradation. All dimensions of climate change exposure were based on present and future predictions of species distributions. Annual mean temperature, mean diurnal temperature range, mean temperature of the wettest quarter, precipitation during the wettest quarter, and precipitation seasonality prove the most important variables for otters. All species are vulnerable to climate change, with global vulnerability index ranging from -0,19 for Lontra longicaudis to -36,9 for Aonyx congicus. However, we found that, for a given species, climate change can have both positive and negative effects on different components of extrinsic exposure, and that measures of species’ sensitivity are not necessarily congruent with measures of exposure. For instance, the range of all African species would be negatively affected by climate change, but their different sensitivity offers a more (Hydrictis maculicollis, Aonyx capensis) or less (Aonyx congicus) pessimistic perspective on their ability to cope with climate change. Also, highly sensitive species like the South-American Pteronura brasiliensis, Lontra provocax, and Lutra perspicillata might face no exposure to climate change. For the Asian Lutra sumatrana, climate change would instead lead to an increased, less fragmented, and more protected range extent, but the range extent would also be shifted into areas with higher human disturbances. Our study represents a balanced example of how to develop an index aimed at comparatively evaluating vulnerability to climate change of different species by combining different aspects of sensitivity and exposure, providing additional information on which to base more efficient conservation strategies

Matter in Loop Quantum Gravity without time gauge: a non-minimally coupled scalar field

We analyze the phase space of gravity non-minimally coupled to a scalar field in a generic local Lorentz frame. We reduce the set of constraints to a first-class one by fixing a specific hypersurfaces in the phase space. The main issue of our analysis is to extend the features of the vacuum case to the presence of scalar matter by recovering the emergence of an SU(2) gauge structure and the non-dynamical role of boost variables. Within this scheme, the super-momentum and the super-Hamiltonian are those ones associated with a scalar field minimally coupled to the metric in the Einstein frame. Hence, the kinematical Hilbert space is defined as in canonical Loop Quantum Gravity with a scalar field, but the differences in the area spectrum are outlined to be the same as in the time-gauge approach.Comment: 6 page

E.C.G. Stueckelberg: a forerunner of modern physics II

We will investigate some aspects of Stueckelberg's work, which have contributed to the development of modern physics. On the one hand, the definition of diffuse boundaries in the calculation of scattering amplitudes will be reviewed, and compared with the other proposals by physicists of that time. On the other hand, the applications of Stueckelberg's description of a massive vector field in the Standard Model will be discussed.Comment: 8 pages, no figures, to appear in Proceedings of the II Stueckelberg Workshop - Int. J. Mod. Phys.

Spatial modelling of soil water holding capacity improves models of plant distributions in mountain landscapes

Aims The aims of this study were: 1) to test a new methodology to overcome the issue of the predictive capacity of soil water availability in geographic space due to measurement scarcity, 2) to model and generalize soil water availability spatially to a whole region, and 3) to test its predictive capacity in plant SDMs. Methods First, we modelled the measured Soil Water Holding Capacity (SWHC at different pFs) of 24 soils in a focal research area, using a weighted ensemble of small bivariate models (ESM). We then used these models to predict 256 locations of a larger region and used the differences in these pF predictions to calculate three different indices of soil water availability for plants (SWAP. These SWAP variables were added one by one to a set of conventional topo-climatic predictors to model 104 plant species distributions. Results We showed that adding SWAP to the SDMs could improve our ability to predict plant species distributions, and more specifically, pF1.8–pF4.2 became the third most important predictor across all plant models. Conclusions Soil water availability can contribute a significant increase in the predictive power of plant distribution models, by identifying important additional abiotic information to describe plant ecological niches

General Relativity as Classical Limit of Evolutionary Quantum Gravity

We analyze the dynamics of the gravitational field when the covariance is restricted to a synchronous gauge. In the spirit of the Noether theorem, we determine the conservation law associated to the Lagrangian invariance and we outline that a non-vanishing behavior of the Hamiltonian comes out. We then interpret such resulting non-zero ``energy'' of the gravitational field in terms of a dust fluid. This new matter contribution is co-moving to the slicing and it accounts for the ``materialization'' of a synchronous reference from the corresponding gauge condition. Further, we analyze the quantum dynamics of a generic inhomogeneous Universe as described by this evolutionary scheme, asymptotically to the singularity. We show how the phenomenology of such a model overlaps the corresponding Wheeler-DeWitt picture. Finally, we study the possibility of a Schr\"odinger dynamics of the gravitational field as a consequence of the correspondence inferred between the ensemble dynamics of stochastic systems and the WKB limit of their quantum evolution. We demonstrate that the time dependence of the ensemble distribution is associated with the first order correction in $\hbar$ to the WKB expansion of the energy spectrum.Comment: 23 pages, to appear on Class. Quant. Gra