Is there a Jordan geometry underlying quantum physics?

There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such approaches: there is a ``Jordan geometry'' belonging to the Jordan part of the algebra of observables, in the same way as Lie groups belong to the Lie part. Both the Lie geometry and the Jordan geometry are well-adapted to describe certain features of quantum theory. We concentrate here on the mathematical description of the Jordan geometry and raise some questions concerning possible relations with foundational issues of quantum theory.Comment: 30 page

Two dimensional Sen connections and quasi-local energy-momentum

The recently constructed two dimensional Sen connection is applied in the problem of quasi-local energy-momentum in general relativity. First it is shown that, because of one of the two 2 dimensional Sen--Witten identities, Penrose's quasi-local charge integral can be expressed as a Nester--Witten integral.Then, to find the appropriate spinor propagation laws to the Nester--Witten integral, all the possible first order linear differential operators that can be constructed only from the irreducible chiral parts of the Sen operator alone are determined and examined. It is only the holomorphy or anti-holomorphy operator that can define acceptable propagation laws. The 2 dimensional Sen connection thus naturally defines a quasi-local energy-momentum, which is precisely that of Dougan and Mason. Then provided the dominant energy condition holds and the 2-sphere S is convex we show that the next statements are equivalent: i. the quasi-local mass (energy-momentum) associated with S is zero; ii.the Cauchy development $D(\Sigma)$ is a pp-wave geometry with pure radiation ($D(\Sigma)$ is flat), where $\Sigma$ is a spacelike hypersurface whose boundary is S; iii. there exist a Sen--constant spinor field (two spinor fields) on S. Thus the pp-wave Cauchy developments can be characterized by the geometry of a two rather than a three dimensional submanifold.Comment: 20 pages, Plain Tex, I

Holography, Unfolding and Higher-Spin Theory

Holographic duality is argued to relate classes of models that have equivalent unfolded formulation, hence exhibiting different space-time visualizations for the same theory. This general phenomenon is illustrated by the $AdS_4$ higher-spin gauge theory shown to be dual to the theory of 3d conformal currents of all spins interacting with 3d conformal higher-spin fields of Chern-Simons type. Generally, the resulting 3d boundary conformal theory is nonlinear, providing an interacting version of the 3d boundary sigma model conjectured by Klebanov and Polyakov to be dual to the $AdS_4$ HS theory in the large $N$ limit. Being a gauge theory it escapes the conditions of the theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory to be free. Two reductions of particular higher-spin gauge theories where boundary higher-spin gauge fields decouple from the currents and which have free boundary duals are identified. Higher-spin holographic duality is also discussed for the cases of $AdS_3/CFT_2$ and duality between higher-spin theories and nonrelativistic quantum mechanics. In the latter case it is shown in particular that ($dS$) $AdS$ geometry in the higher-spin setup is dual to the (inverted) harmonic potential in the quantum-mechanical setup.Comment: 57 pages, V2: Acknowledgements, references, comments, clarifications and new section on reductions of particular HS theories associated with free boundary theories are added. Typos corrected, V3. Minor corrections: clarification in section 9 is added and typos correcte

Two dimensional Sen connections in general relativity

The two dimensional version of the Sen connection for spinors and tensors on spacelike 2-surfaces is constructed. A complex metric $\gamma_{AB}$ on the spin spaces is found which characterizes both the algebraic and extrinsic geometrical properties of the 2-surface $\$$. The curvature of the two dimensional Sen operator $\Delta_e$ is the pull back to $\$$ of the anti-self-dual part of the spacetime curvature while its `torsion' is a boost gauge invariant expression of the extrinsic curvatures of $\$$. The difference of the 2 dimensional Sen and the induced spin connections is the anti-self-dual part of the `torsion'. The irreducible parts of $\Delta_e$ are shown to be the familiar 2-surface twistor and the Weyl--Sen--Witten operators. Two Sen--Witten type identities are derived, the first is an identity between the 2 dimensional twistor and the Weyl--Sen--Witten operators and the integrand of Penrose's charge integral, while the second contains the `torsion' as well. For spinor fields satisfying the 2-surface twistor equation the first reduces to Tod's formula for the kinematical twistor.Comment: 14 pages, Plain Tex, no report numbe

From 2D conformal to 4D self-dual theories: quaternionic analyticity

It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity (natural in two dimensions) to quaternionic analyticity (natural in four dimensions). To be analytic, conformal transformations should be realized on $CP^3$, which appears as the coset of the complexified conformal group modulo its maximal parabolic subgroup. In this language one visualizes the twistor correspondence of Penrose and Ward and consistently formulates the analyticity of Fueter.Comment: 24 pages, LaTe

Womens' opinions on antenatal care in developing countries: results of a study in Cuba, Thailand, Saudi Arabia and Argentina

BACKGROUND: The results of a qualitative study carried out in four developing countries (Cuba, Thailand, Saudi Arabia and Argentina) are presented. The study was conducted in the context of a randomised controlled trial to test the benefits of a new antenatal care protocol that reduced the number of visits to the doctor, rationalised the application of technology, and improved the provision of information to women in relation to the traditional protocol applied in each country. METHODS: Through focus groups discussions we were able to assess the concepts and expectations underlying women's evaluation of concepts and experiences of the care received in antenatal care clinics. 164 women participated in 24 focus groups discussion in all countries. RESULTS: Three areas are particularly addressed in this paper: a) concepts about pregnancy and health care, b) experience with health services and health providers, and c) opinions about the modified Antenatal Care (ANC) programme. In all three topics similarities were identified as well as particular opinions related to country specific social and cultural values. In general women have a positive view of the new ANC protocol, particularly regarding the information they receive. However, controversial issues emerged such as the reduction in the number of visits, particularly in Cuba where women are used to have 18 ANC visits in one pregnancy period. CONCLUSION: Recommendations to improve ANC services performance are being proposed. Any country interested in the application of a new ANC protocol should regard the opinion and acceptability of women towards changes

Neurodevelopment Genes in Lampreys Reveal Trends for Forebrain Evolution in Craniates

The forebrain is the brain region which has undergone the most dramatic changes through vertebrate evolution. Analyses conducted in lampreys are essential to gain insight into the broad ancestral characteristics of the forebrain at the dawn of vertebrates, and to understand the molecular basis for the diversifications that have taken place in cyclostomes and gnathostomes following their splitting. Here, we report the embryonic expression patterns of 43 lamprey genes, coding for transcription factors or signaling molecules known to be involved in cell proliferation, stemcellness, neurogenesis, patterning and regionalization in the developing forebrain. Systematic expression patterns comparisons with model organisms highlight conservations likely to reflect shared features present in the vertebrate ancestors. They also point to changes in signaling systems –pathways which control the growth and patterning of the neuroepithelium-, which may have been crucial in the evolution of forebrain anatomy at the origin of vertebrates

Tales of the unexpected: the selection of British party leaders since 1963

Jeremy Corbyn’s election as Leader of the Labour Party in 2015 stunned observers and practitioners of British politics alike. In this article, we first outline a theoretical framework that purports to explain why political parties operating in parliamentary systems choose the leaders they do. We then examine 32 leadership successions involving five major British parties since 1963, and note that many of these were unexpected, in that they were triggered by unforeseen circumstances, such as the sudden death or resignation of the incumbent. Examining each party in turn, we briefly explain why the winners won and identify at least eight cases (a quarter of our sample) where a candidate widely expected to prevail at the outset was ultimately defeated by a ‘dark horse’, ‘second favourite’ or even ‘rank outsider’. Of these, Corbyn’s election in 2015 was the most unexpected and, consistent with the findings of studies of party leadership conventions in other parliamentary systems, namely Canada and Spain, suggests that ideological and policy concerns are sometimes more important than considerations of party unity and electability, especially when a leadership contest is dominated by party activists