Scalar Field Theory on Non-commutative Snyder Space-Time

We construct a scalar field theory on the Snyder non-commutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincar\'e algebra is undeformed. The Lorentz sector is undeformed at both algebraic and co-algebraic level, but the co-product for momenta (defining the star-product) is non-co-associative. The Snyder-deformed Poincar\'e group is described by a non-co-associative Hopf algebra. The definition of the interacting theory in terms of a non-associative star-product is thus questionable. We avoid the non-associativity by the use of a space-time picture based on the concept of realization of a non-commutative geometry. The two main results we obtain are: (i) the generic (namely for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a non-ambiguous self interacting scalar field theory on this space-time. The first order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.Comment: 10 pages; v2: introduction rewritten, co-algebraic analysis improved, references added; to appear in PR

Wodzicki Residue for Operators on Manifolds with Cylindrical Ends

We define the Wodzicki Residue TR(A) for A in a space of operators with double order (m_1,m_2). Such operators are globally defined initially on R^n and then, more generally, on a class of non-compact manifolds, namely, the manifolds with cylindrical ends. The definition is based on the analysis of the associate zeta function. Using this approach, under suitable ellipticity assumptions, we also compute a two terms leading part of the Weyl formula for a positive selfadjoint operator belonging the mentioned class in the case m_1=m_2.Comment: 24 pages, picture changed, added references, corrected typo

ENSO in the Mid-Holocene according to CSM and HadCM3

The offline linearized ocean–atmosphere model (LOAM), which was developed to quantify the impact of the climatological mean state on the variability of the El Niño–Southern Oscillation (ENSO), is used to illuminate why ENSO changed between the modern-day and early/mid-Holocene simulations in two climate modeling studies using the NCAR Climate System Model (CSM) and the Hadley Centre Coupled Model, version 3 (HadCM3). LOAM reproduces the spatiotemporal variability simulated by the climate models and shows both the reduction in the variance of ENSO and the changes in the spatial structure of the variance during the early/mid-Holocene. The mean state changes that are important in each model are different and, in both cases, are also different from those hypothesized to be important in the original papers describing these simulations. In the CSM simulations, the ENSO mode is stabilized by the mean cooling of the SST. This reduces atmospheric heating anomalies that in turn give smaller wind stress anomalies, thus weakening the Bjerknes feedback. Within the ocean, a change in the thermocline structure alters the spatial pattern of the variance, shifting the peak variance farther east, but does not reduce the overall amount of ENSO variance. In HadCM3, the ENSO mode is stabilized by a combination of a weaker thermocline and weakened horizontal surface currents. Both of these reduce the Bjerknes feedback by reducing the ocean’s SST response to wind stress forcing. This study demonstrates the importance of considering the combined effect of a mean state change on the coupled ocean–atmosphere system: conflicting and erroneous results are obtained for both models if only one model component is considered in isolation

Many-nodes/many-links spinfoam: the homogeneous and isotropic case

I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry. This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the compete graph on 5 nodes. All the resulting amplitudes have the same support, independently of the graph used, in the large j (large volume) limit. This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant. This result indicates that in the semiclassical limit quantum corrections in spinfoam cosmology do not come from just refining the graph, but rather from relaxing the large j limit.Comment: 8 pages, 4 figure

Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case.Comment: 11 page

Climate Engineering Responses to Climate Emergencies

Despite efforts to stabilize CO_2 concentrations, it is possible that the climate system could respond abruptly with catastrophic consequences. Intentional intervention in the climate system to avoid or ameliorate such consequences has been proposed as one possible response, should such a scenario arise. In a one-week study, the authors of this report conducted a technical review and evaluation of proposed climate engineering concepts that might serve as a rapid palliative response to such climate emergency scenarios. Because of their potential to induce a prompt (less than one year) global cooling, this study concentrated on Shortwave Climate Engineering (SWCE) methods for moderately reducing the amount of shortwave solar radiation reaching the Earth. The study's main objective was to outline a decade-long agenda of technical research that would maximally reduce the uncertainty surrounding the benefits and risks associated with SWCE. For rigor of technical analysis, the study focused the research agenda on one particular SWCE concept--stratospheric aerosol injection--and in doing so developed several conceptual frameworks and methods valuable for assessing any SWCE proposal.Comment: 66 pp., 5 figs., published by Novim, Santa Barbara, Cal., revised referenc