Two-particle irreducible effective actions versus resummation: analytic properties and self-consistency

Approximations based on two-particle irreducible (2PI) effective actions (also known as $\Phi$-derivable, Cornwall-Jackiw-Tomboulis or Luttinger-Ward functionals depending on context) have been widely used in condensed matter and non-equilibrium quantum/statistical field theory because this formalism gives a robust, self-consistent, non-perturbative and systematically improvable approach which avoids problems with secular time evolution. The strengths of 2PI approximations are often described in terms of a selective resummation of Feynman diagrams to infinite order. However, the Feynman diagram series is asymptotic and summation is at best a dangerous procedure. Here we show that, at least in the context of a toy model where exact results are available, the true strength of 2PI approximations derives from their self-consistency rather than any resummation. This self-consistency allows truncated 2PI approximations to capture the branch points of physical amplitudes where adjustments of coupling constants can trigger an instability of the vacuum. This, in effect, turns Dyson's argument for the failure of perturbation theory on its head. As a result we find that 2PI approximations perform better than Pad\'e approximation and are competitive with Borel-Pad\'e resummation. Finally, we introduce a hybrid 2PI-Pad\'e method.Comment: Version accepted for publication in Nuclear Physics B. 31 pages, 16 figures. Uses feynm

The use of some Gaelic songs and poetry in <i>The Cheviot, the Stag and the Black Black Oil</i>

No abstract available

The bimodal color distribution of small Kuiper Belt objects

We conducted a two-night photometric survey of small Kuiper Belt objects (KBOs) near opposition using the wide-field Hyper Suprime-Cam instrument on the 8.2 m Subaru Telescope. The survey covered about 90 deg^2 of sky, with each field imaged in the g and i bands. We detected 356 KBOs, ranging in absolute magnitude from 6.5 to 10.4. Filtering for high-inclination objects within the hot KBO population, we show that the g-i color distribution is strongly bimodal, indicative of two color classes - the red and very red subpopulations. After categorizing objects into the two subpopulations by color, we present the first dedicated analysis of the magnitude distributions of the individual color subpopulations and demonstrate that the two distributions are roughly identical in shape throughout the entire size range covered by our survey. Comparing the color distribution of small hot KBOs with that of Centaurs, we find that they have similar bimodal shapes, thereby providing strong confirmation of previous explanations for the attested bimodality of Centaurs. We also show that the magnitude distributions of the two KBO color subpopulations and the two color subpopulations observed in the Jupiter Trojans are statistically indistinguishable. Finally, we discuss a hypothesis describing the origin of the KBO color bimodality based on our survey results.Comment: 9 pages, 6 figures, accepted for publication in AJ, supplemental table accessible on online journa

Multiband photometry of a Patroclus-Menoetius mutual event: Constraints on surface heterogeneity

We present the first complete multiband observations of a binary asteroid mutual event. We obtained high-cadence, high-signal-to-noise photometry of the UT 2018 April 9 inferior shadowing event in the Jupiter Trojan binary system Patroclus-Menoetius in four Sloan bands $-$ $g'$, $r'$, $i'$, and $z'$. We use an eclipse lightcurve model to fit for a precise mid-eclipse time and estimate the minimum separation of the two eclipsing components during the event. Our best-fit mid-eclipse time of $2458217.80943^{+0.00057}_{-0.00050}$ is 19 minutes later than the prediction of Grundy et al. (2018); the minimum separation between the center of Menoetius' shadow and the center of Patroclus is $72.5\pm0.7$ km $-$ slightly larger than the predicted 69.5 km. Using the derived lightcurves, we find no evidence for significant albedo variations or large-scale topographic features on the Earth-facing hemisphere and limb of Patroclus. We also apply the technique of eclipse mapping to place an upper bound of $\sim$0.15 mag on wide-scale surface color variability across Patroclus.Comment: 5 pages, 3 figures, accepted for publication in A

Groups of type FPFP via graphical small cancellation

We construct an uncountable family of groups of type $FP$. In contrast to every previous construction of non-finitely presented groups of type $FP$ we do not use Morse theory on cubical complexes; instead we use Gromov's graphical small cancellation theory.Comment: 3 figures. Second version: two paragraphs added emphasizing the difference between our construction and Morse theoretic one

A hypothesis for the color bimodality of Jupiter Trojans

One of the most enigmatic and hitherto unexplained properties of Jupiter Trojans is their bimodal color distribution. This bimodality is indicative of two sub-populations within the Trojans, which have distinct size distributions. In this paper, we present a simple, plausible hypothesis for the origin and evolution of the two Trojan color sub-populations. In the framework of dynamical instability models of early Solar System evolution, which suggest a common primordial progenitor population for both Trojans and Kuiper belt objects, we use observational constraints to assert that the color bimodalities evident in both minor body populations developed within the primordial population prior to the onset of instability. We show that, beginning with an initial composition of rock and ices, location-dependent volatile loss through sublimation in this primordial population could have led to sharp changes in the surface composition with heliocentric distance. We propose that the depletion or retention of H$_{2}$S ice on the surface of these objects was the key factor in creating an initial color bimodality. Objects that retained H$_{2}$S on their surfaces developed characteristically redder colors upon irradiation than those that did not. After the bodies from the primordial population were scattered and emplaced into their current positions, they preserved this primordial color bimodality to the present day. We explore predictions of the volatile loss model - in particular, the effect of collisions within the Trojan population on the size distributions of the two sub-populations - and propose further experimental and observational tests of our hypothesisComment: 8 pages, 3 figures, accepted for publication in A

SKA Engineering Change Proposal: Gridded Visibilities to Enable Precision Cosmology with Radio Weak Lensing

This document was submitted as supporting material to an Engineering Change Proposal (ECP) for the Square Kilometre Array (SKA). This ECP requests gridded visibilities as an extra imaging data product from the SKA, in order to enable bespoke analysis techniques to measure source morphologies to the accuracy necessary for precision cosmology with radio weak lensing. We also discuss the properties of an SKA weak lensing data set and potential overlaps with other cosmology science goals.Comment: Comments welcome. 4 pages, 3 figures. Progress can be tracked at the SKA ECP register https://skaoffice.atlassian.net/wiki/display/EP/ECP+Registe