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

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

Encounters with racism and the international student experience

This article makes a contribution to the existing and extensive literature on the international student experience by reporting on the incidence of racism and religious incidents experienced by international students at a university in the south of England. Out of a survey of 153 international postgraduate students, 49 had experienced some form of abuse. In most cases, this took the form of verbal abuse though racism manifested physically for nine students. Strong emotional reactions were reported, including sadness, disappointment, homesickness and anger. There was a consequent reluctance to return to the UK as a leisure tourist or to offer positive word of mouth to future students. This article offers a portrait of the reception offered to international students against a backdrop of increased racism in the UK. A link is thus made between the micro experience and macro forces. Implications of racist abuse for student satisfaction and future international student recruitment are drawn