Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory

The present paper studies the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical configurations. Here we show that, given a critical configuration in general, there exists a partition of the simplicial complex into three type of regions R_{Nondeg}, R_{Deg-A}, R_{Deg-B}, where the three regions are simplicial sub-complexes with boundaries. The critical configuration implies different types of geometries in different types of regions, i.e. (1) the critical configuration restricted into R_{Nondeg}$implies a nondegenerate discrete Lorentzian geometry, (2) the critical configuration restricted into R_{Deg-A}$ is degenerate of type-A in our definition of degeneracy, but implies a nondegenerate discrete Euclidean geometry on R_{Deg-A}, (3) the critical configuration restricted into R_{Deg-B} is degenerate of type-B, and implies a vector geometry on R_{Deg-B}. With the critical configuration, we further make a subdivision of the regions R_{Nondeg} and R_{Deg-A} into sub-complexes (with boundary) according to their Lorentzian/Euclidean oriented 4-simplex volume V_4(v), such that sgn(V_4(v)) is a constant sign on each sub-complex. Then in the each sub-complex, the spinfoam amplitude at the critical configuration gives the Regge action in Lorentzian or Euclidean signature respectively on R_{Nondeg} or R_{Deg-A}. The Regge action reproduced here contains a sign factor sgn(V_4(v)) of the oriented 4-simplex volume. Therefore the Regge action reproduced here can be viewed a discretized Palatini action with on-shell connection. Finally the asymptotic formula of the spinfoam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.Comment: 54 pages, 2 figures, reference adde

Astrometric Resolution of Severely Degenerate Binary Microlensing Events

We investigate whether the "close/wide" class of degeneracies in caustic-crossing binary microlensing events can be broken astrometrically. Dominik showed that these degeneracies are particularly severe because they arise from a degeneracy in the lens equation itself rather than a mere "accidental" mimicking of one light curve by another. A massive observing campaign of five microlensing collaborations was unable to break this degeneracy photometrically in the case of the binary lensing event MACHO 98-SMC-1. We show that this degeneracy indeed causes the image centroids of the wide and close solutions to follow an extremely similar pattern of motion during the time when the source is in or near the caustic. Nevertheless, the two image centroids are displaced from one another and this displacement is detectable by observing the event at late times. Photometric degeneracies therefore can be resolved astrometrically, even for these most severe cases.Comment: 11 pages, including 4 figures. Submitted to Ap

Low-amplitude and long-period radial velocity variations in giants HD 3574, 63 Cygni, and HD 216946 (Research Note)

Aims. We study the low-amplitude and long-period variations in evolved stars using precise radial velocity measurements. Methods. The high-resolution, fiber-fed Bohyunsan Observatory Echelle Spectrograph (BOES) was used from September 2004 to May 2014 as part of the exoplanet search program at the Bohyunsan Optical Astronomy Observatory (BOAO). Results. We report the detection of low-amplitude and long-period orbital radial velocity variations in three evolved stars, HD 3574, 63 Cyg, and HD 216946. They have periods of 1061, 982, and 1382 days and semi-amplitudes of 376, 742, and 699 m/s, respectively.Comment: 6 pages, 7 figures, 4 tables, accepted for publisation in Astronomy & Astrophysic

Women’s facial attractiveness is related to their body mass index, but not their salivary cortisol

Objectives: Although many theories of human facial attractiveness propose positive correlations between facial attractiveness and measures of actual health, evidence for such correlations is somewhat mixed. Here we sought to replicate a recent study reporting that women’s facial attractiveness is independently related to both their adiposity and cortisol. Methods: Ninety-six women provided saliva samples, which were analyzed for cortisol level, and their height and weight, which were used to calculate their body mass index (BMI). A digital face image of each woman was also taken under standardized photographic conditions and rated for attractiveness. Results: There was a significant negative correlation between women’s facial attractiveness and BMI. By contrast, salivary cortisol and facial attractiveness were not significantly correlated. Conclusions: Our results suggest that the types of health information reflected in women's faces include qualities that are indexed by BMI, but do not necessarily include qualities that are indexed by cortisol

Commuting Simplicity and Closure Constraints for 4D Spin Foam Models

Spin Foam Models are supposed to be discretised path integrals for quantum gravity constructed from the Plebanski-Holst action. The reason for there being several models currently under consideration is that no consensus has been reached for how to implement the simplicity constraints. Indeed, none of these models strictly follows from the original path integral with commuting B fields, rather, by some non standard manipulations one always ends up with non commuting B fields and the simplicity constraints become in fact anomalous which is the source for there being several inequivalent strategies to circumvent the associated problems. In this article, we construct a new Euclidian Spin Foam Model which is constructed by standard methods from the Plebanski-Holst path integral with commuting B fields discretised on a 4D simplicial complex. The resulting model differs from the current ones in several aspects, one of them being that the closure constraint needs special care. Only when dropping the closure constraint by hand and only in the large spin limit can the vertex amplitudes of this model be related to those of the FK Model but even then the face and edge amplitude differ. Curiously, an ad hoc non-commutative deformation of the $B^{IJ}$ variables leads from our new model to the Barrett-Crane Model in the case of Barbero-Immirzi parameter goes to infinity.Comment: 41 pages, 4 figure

Local spinfoam expansion in loop quantum cosmology

The quantum dynamics of the flat Friedmann-Lemaitre-Robertson-Walker and Bianchi I models defined by loop quantum cosmology have recently been translated into a spinfoam-like formalism. The construction is facilitated by the presence of a massless scalar field which is used as an internal clock. The implicit integration over the matter variable leads to a nonlocal spinfoam amplitude. In this paper we consider a vacuum Bianchi I universe and show that by choosing an appropriate regulator a spinfoam expansion can be obtained without selecting a clock variable and that the resulting spinfoam amplitude is local.Comment: 12 page