Metric projective geometry, BGG detour complexes and partially massless gauge theories

A projective geometry is an equivalence class of torsion free connections sharing the same unparametrised geodesics; this is a basic structure for understanding physical systems. Metric projective geometry is concerned with the interaction of projective and pseudo-Riemannian geometry. We show that the BGG machinery of projective geometry combines with structures known as Yang-Mills detour complexes to produce a general tool for generating invariant pseudo-Riemannian gauge theories. This produces (detour) complexes of differential operators corresponding to gauge invariances and dynamics. We show, as an application, that curved versions of these sequences give geometric characterizations of the obstructions to propagation of higher spins in Einstein spaces. Further, we show that projective BGG detour complexes generate both gauge invariances and gauge invariant constraint systems for partially massless models: the input for this machinery is a projectively invariant gauge operator corresponding to the first operator of a certain BGG sequence. We also connect this technology to the log-radial reduction method and extend the latter to Einstein backgrounds.Comment: 30 pages, LaTe

Quantum Gravity and Causal Structures: Second Quantization of Conformal Dirac Algebras

It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum gravity models by quantizing the moduli of Laplace, weight and defining-function operators on Fefferman-Graham ambient spaces. The algebra of these operators underlies conformal geometries. We extend those results to include fermions by taking an osp(1|2) "Dirac square root" of these algebras. The theory is a simple, Grassmann, two-matrix model. Its quantum action is a Chern-Simons theory whose differential is a first-quantized, quantum mechanical BRST operator. The theory is a basic ingredient for building fundamental theories of physical observables.Comment: 4 pages, LaTe

Charge dynamics in molecular junctions: Nonequilibrium Green's Function approach made fast

Real-time Green's function simulations of molecular junctions (open quantum systems) are typically performed by solving the Kadanoff-Baym equations (KBE). The KBE, however, impose a serious limitation on the maximum propagation time due to the large memory storage needed. In this work we propose a simplified Green's function approach based on the Generalized Kadanoff-Baym Ansatz (GKBA) to overcome the KBE limitation on time, significantly speed up the calculations, and yet stay close to the KBE results. This is achieved through a twofold advance: first we show how to make the GKBA work in open systems and then construct a suitable quasi-particle propagator that includes correlation effects in a diagrammatic fashion. We also provide evidence that our GKBA scheme, although already in good agreement with the KBE approach, can be further improved without increasing the computational cost.Comment: 13 pages, 13 figure

The qq-linked complex Minkowski space, its real forms and deformed isometry groups

We establish duality between real forms of the quantum deformation of the 4-dimensional orthogonal group studied by Fioresi et al. and the classification work made by Borowiec et al.. Classically these real forms are the isometry groups of $\mathbb{R}^4$ equipped with Euclidean, Kleinian or Lorentzian metric. A general deformation, named $q$-linked, of each of these spaces is then constructed, together with the coaction of the corresponding isometry group.Comment: 25 pages, discussion improved, bibliography update

The symplectic origin of conformal and Minkowski superspaces

Supermanifolds provide a very natural ground to understand and handle supersymmetry from a geometric point of view; supersymmetry in $d=3,4,6$ and $10$ dimensions is also deeply related to the normed division algebras. In this paper we want to show the link between the conformal group and certain types of symplectic transformations over division algebras. Inspired by this observation we then propose a new\,realization of the real form of the 4 dimensional conformal and Minkowski superspaces we obtain, respectively, as a Lagrangian supermanifold over the twistor superspace $\mathbb{C}^{4|1}$ and a big cell inside it. The beauty of this approach is that it naturally generalizes to the 6 dimensional case (and possibly also to the 10 dimensional one) thus providing an elegant and uniform characterization of the conformal superspaces.Comment: 15 pages, references added, minor change

New insight into WDVV equation

We show that Witten-Dijkgraaf-Verlinde-Verlinde equation underlies the construction of N=4 superconformal multi--particle mechanics in one dimension, including a N=4 superconformal Calogero model.Comment: 16 pages, no figures, LaTeX file, PACS: 04.60.Ds; 11.30.P

Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics

Fefferman and Graham showed some time ago that four dimensional conformal geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit systems. Strikingly, Einstein's equations are then equivalent to the existence of a parallel scale tractor (a six component vector subject to a certain first order covariant constancy condition at every point in four dimensional spacetime). These results suggest a six dimensional description of four dimensional physics, a viewpoint promulgated by the two times physics program of Bars. The Fefferman--Graham construction relies on a triplet of operators corresponding, respectively to a curved six dimensional light cone, the dilation generator and the Laplacian. These form an sp(2) algebra which Bars employs as a first class algebra of constraints in a six-dimensional gauge theory. In this article four dimensional gravity is recast in terms of six dimensional quantum mechanics by melding the two times and tractor approaches. This "parent" formulation of gravity is built from an infinite set of six dimensional fields. Successively integrating out these fields yields various novel descriptions of gravity including a new four dimensional one built from a scalar doublet, a tractor vector multiplet and a conformal class of metrics.Comment: 27 pages, LaTe

Local attitudes toward Apennine brown bears: Insights for conservation issues

Human-carnivore coexistence is a multi-faceted issue that requires an understanding of the diverse attitudes and perspectives of the communities living with large carnivores. To inform initiatives that encourage behaviors in line with conservation goals, we focused on assessing the two components of attitudes (i.e., feelings and beliefs), as well as norms of local communities coexisting with Apennine brown bears (Ursus arctos marsicanus) for a long time. This bear population is under serious extinction risks due to its persistently small population size, which is currently confined to the long-established protected area of Abruzzo, Lazio and Molise National Park (PNALM) and its surrounding region in central Italy. We interviewed 1,611 residents in the PNALM to determine attitudes and values toward bears. We found that support for the bear's legal protection was widespread throughout the area, though beliefs about the benefits of conserving bears varied across geographic administrative districts. Our results showed that residents across our study areas liked bears. At the same time, areas that received more benefits from tourism were more strongly associated with positive feelings toward bears. Such findings provide useful information to improve communication efforts of conservation authorities with local communities

Spinal Anesthesia and Minimal Invasive Laminotomy for Paddle Electrode Placement in Spinal Cord Stimulation: Technical Report and Clinical Results at Long-Term Followup

Object. We arranged a mini-invasive surgical approach for implantation of paddle electrodes for SCS under spinal anesthesia obtaining the best paddle electrode placement and minimizing patients' discomfort. We describe our technique supported by neurophysiological intraoperative monitoring and clinical results. Methods. 16 patients, affected by neuropathic pain underwent the implantation of paddle electrodes for spinal cord stimulation in lateral decubitus under spinal anesthesia. The paddle was introduced after flavectomy and each patient confirmed the correct distribution of paresthesias induced by intraoperative test stimulation. VAS and patients' satisfaction rate were recorded during the followup and compared to preoperative values. Results. No patients reported discomfort during the procedure. In all cases, paresthesias coverage of the total painful region was achieved, allowing the best final electrode positioning. At the last followup (mean 36.7 months), 87.5% of the implanted patients had a good rate of satisfaction with a mean VAS score improvement of 70.5%. Conclusions. Spinal cord stimulation under spinal anesthesia allows an optimal positioning of the paddle electrodes without any discomfort for patients or neurosurgeons. The best intraoperative positioning allows a better postoperative control of pain, avoiding the risk of blind placements of the paddle or further surgery for their replacement