Conformal covariance of massless free nets

In the present paper we review in a fibre bundle context the covariant and massless canonical representations of the Poincare' group as well as certain unitary representations of the conformal group (in 4 dimensions). We give a simplified proof of the well-known fact that massless canonical representations with discrete helicity extend to unitary and irreducible representations of the conformal group mentioned before. Further we give a simple new proof that massless free nets for any helicity value are covariant under the conformal group. Free nets are the result of a direct (i.e. independent of any explicit use of quantum fields) and natural way of constructing nets of abstract C*-algebras indexed by open and bounded regions in Minkowski space that satisfy standard axioms of local quantum physics. We also give a group theoretical interpretation of the embedding {\got I} that completely characterizes the free net: it reduces the (algebraically) reducible covariant representation in terms of the unitary canonical ones. Finally, as a consequence of the conformal covariance we also mention for these models some of the expected algebraic properties that are a direct consequence of the conformal covariance (essential duality, PCT--symmetry etc.).Comment: 31 pages, Latex2

How Skillful are the Multiannual Forecasts of Atlantic Hurricane Activity?

The recent emergence of near-term climate prediction, wherein climate models are initialized with the contemporaneous state of the Earth system and integrated up to 10 years into the future, has prompted the development of three different multiannual forecasting techniques of North Atlantic hurricane frequency. Descriptions of these three different approaches, as well as their respective skill, are available in the peer-reviewed literature, but because these various studies are sufficiently different in their details (e.g., period covered, metric used to compute the skill, measure of hurricane activity), it is nearly impossible to compare them. Using the latest decadal reforecasts currently available, we present a direct comparison of these three multiannual forecasting techniques with a combination of simple statistical models, with the hope of offering a perspective on the current state-of-the-art research in this field and the skill level currently reached by these forecasts. Using both deterministic and probabilistic approaches, we show that these forecast systems have a significant level of skill and can improve on simple alternatives, such as climatological and persistence forecasts.The first author would like to thank Isadora Jimenez for providing the necessary material for Fig. 2. The first author would like to acknowledge the financial support from the Ministerio de Economía, Industria y Competitividad (MINECO; Project CGL2014- 55764-R), the Risk Prediction Initiative at BIOS (Grant RPI2.0-2013-CARON), and the EU [Seventh Framework Programme (FP7); Grant Agreement GA603521]. We additionally acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups for producing and making available their model output. For CMIP, the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. LPC's contract is cofinanced by the MINECO under the Juan de la Cierva Incorporacion postdoctoral fellowship number IJCI-2015-23367. Finally, we thank the National Hurricane Center for making the HURDAT2 data available. All climate model data are available at https://esgf-index1.ceda.ac.uk/projects/esgf-ceda/.Peer ReviewedPostprint (published version

The Minkowski and conformal superspaces

We define complex Minkowski superspace in 4 dimensions as the big cell inside a complex flag supermanifold. The complex conformal supergroup acts naturally on this super flag, allowing us to interpret it as the conformal compactification of complex Minkowski superspace. We then consider real Minkowski superspace as a suitable real form of the complex version. Our methods are group theoretic, based on the real conformal supergroup and its Lie superalgebra.Comment: AMS LaTeX, 44 page

Quantum Chiral Superfields

We define the ordinary Minkowski space inside the conformal space according to Penrose and Manin as homogeneous spaces for the Poincar\'e and conformal group respectively. We realize the supersymmetric (SUSY) generalizations of such homogeneous spaces over the complex and the real fields. We finally investigate chiral (antichiral) superfields, which are superfields on the super Grassmannian, Gr(2|1, 4|1), respectively on Gr(2|0, 4|1). They ultimately give the twistor coordinates necessary to describe the conformal superspace as the flag Fl(2|0, 2|1; 4|1) and the Minkowski superspace as its big cell.Comment: 10 pages. To appear in the proceedings of the ' Avenues of Quantum Field Theory in Curved Spacetime September 14-16, 2022. University of Genova (Italy

Star Products on Coadjoint Orbits

We study properties of a family of algebraic star products defined on coadjoint orbits of semisimple Lie groups. We connect this description with the point of view of differentiable deformations and geometric quantization.Comment: Talk given at the XXIII ICGTMP, Dubna (Russia) August 200

Twisted duality of the CAR-Algebra

We give a complete proof of the twisted duality property M(q)'= Z M(q^\perp) Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two suitable closed subspaces have been distinguished. We use modular theory and techniques developed by Kato concerning pairs of projections in some essential steps of the proof. As a byproduct of the proof we obtain an explicit and simple formula for the graph of the modular operator. This formula can be also applied to fermionic free nets, hence giving a formula of the modular operator for any double cone.Comment: 32 pages, Latex2e, to appear in Journal of Mathematical Physic

Algebraic and Differential Star Products on Regular Orbits of Compact Lie Groups

In this paper we study a family of algebraic deformations of regular coadjoint orbits of compact semisimple Lie groups with the Kirillov Poisson bracket. The deformations are restrictions of deformations on the dual of the Lie algebra. We prove that there are non isomorphic deformations in the family. The star products are not differential, unlike the star products considered in other approaches. We make a comparison with the differential star product canonically defined by Kontsevich's map

Quantum twistors

We compute explicitly a star product on the Minkowski space whose Poisson bracket is quadratic. This star product corresponds to a deformation of the conformal spacetime, whose big cell is the Minkowski spacetime. The description of Minkowski space is made in the twistor formalism and the quantization follows by substituting the classical conformal group by a quantum group.Comment: 47 pages. references added, some parts rewritten. To appear in 'p-adic Numbers, Ultrametric Analysis and Applicarions

Torsion formulation of gravity

We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard formulation of gravity. In this formulation it is possible to couple arbitrary torsion to gauge fields without breaking the gauge invariance.Comment: AMS-LaTeX, 25 pages. Appendices have been eliminated and the necessary concepts have been inroduced in the text. We have added some reference