Low-Energy Lorentz Invariance in Lifshitz Nonlinear Sigma Models

This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group aspects with emphasis on the possibility of emergence of Lorentz invariance at low energies. Contrarily to the perturbative expansion, where in general the Lorentz symmetry restoration is delicate and may depend on stringent fine-tuning, our results provide a more favorable scenario in the large-$N$ framework. We also consider supersymmetric extension in this nonrelativistic situation.Comment: 28 pages, 4 figures, minor clarifications, typos corrected, published versio

Juan Baños de Velasco y Acevedo - Emblems in Everyday Life

A research note on a new acquisition for the Stirling Maxwell Collection of Emblem Books, held at the Special Collections department of the University of Glasgow. This was part of a round table on various other items in this recent acquisition. This research note explores different perspectives that add value to this work, namely the close association of this Spanish work with D. Juan de Austria (its dedicatee) and Portugal

A first look at Weyl anomalies in shape dynamics

One of the more popular objections towards shape dynamics is the suspicion that anomalies in the spatial Weyl symmetry will arise upon quantization. The purpose of this short paper is to establish the tools required for an investigation of the sort of anomalies that can possibly arise. The first step is to adapt to our setting Barnich and Henneaux's formulation of gauge cohomology in the Hamiltonian setting, which serve to decompose the anomaly into a spatial component and time component. The spatial part of the anomaly, i.e. the anomaly in the symmetry algebra itself ($[\Omega, \Omega]\propto \hbar$ instead of vanishing) is given by a projection of the second ghost cohomology of the Hamiltonian BRST differential associated to $\Omega$, modulo spatial derivatives. The temporal part, $[\Omega, H]\propto\hbar$ is given by a different projection of the first ghost cohomology and an extra piece arising from a solution to a functional differential equation. Assuming locality of the gauge cohomology groups involved, this part is always local. Assuming locality for the gauge cohomology groups, using Barnich and Henneaux's results, the classification of Weyl cohomology for higher ghost numbers performed by Boulanger, and following the descent equations, we find a complete characterizations of anomalies in 3+1 dimensions. The spatial part of the anomaly and the first component of the temporal anomaly are always local given these assumptions even in shape dynamics. The part emerging from the solution of the functional differential equations explicitly involves the shape dynamics Hamiltonian, and thus might be non-local. If one restricts this extra piece of the temporal anomaly to be also local, then overall no \emph{local} Weyl anomalies, either temporal or spatial, emerge in the 3+1 case.Comment: 13 pages. v2 Change of phrasing in the abstract to avoid semantic ambiguit

Poincar\'e invariance and asymptotic flatness in Shape Dynamics

Shape Dynamics is a theory of gravity that waives refoliation invariance in favor of spatial Weyl invariance. It is a canonical theory, constructed from a Hamiltonian, 3+1 perspective. One of the main deficits of Shape Dynamics is that its Hamiltonian is only implicitly constructed as a functional of the phase space variables. In this paper, I write down the equations of motion for Shape Dynamics to show that over a curve in phase space representing a Minkowski spacetime, Shape Dynamics possesses Poincar\'e symmetry for appropriate boundary conditions. The proper treatment of such boundary conditions leads us to completely formulate Shape Dynamics for open manifolds in the asymptotically flat case. We study the charges arising in this case and find a new definition of total energy, which is completely invariant under spatial Weyl transformations close to the boundary. We then use the equations of motion once again to find a non-trivial solution of Shape Dynamics, consisting of a flat static Universe with a point-like mass at the center. We calculate its energy through the new formula and rederive the usual Schwarzschild mass.Comment: 22 pages, matches accepted versio

Kant, the Philosophy of Mind, and Twentieth-Century Analytic Philosophy

In the first part of this chapter, I summarise some of the issues in the philosophy of mind which are addressed in Kant’s Critical writings. In the second part, I chart some of the ways in which that discussion influenced twentieth-century analytic philosophy of mind and identify some of the themes which characterise Kantian approaches in the philosophy of mind

Perception, Evidence, and our Expressive Knowledge of Others' Minds.

‘How, then, she had asked herself, did one know one thing or another thing about people, sealed as they were?’ So asks Lily Briscoe in To the Lighthouse. It is this question, rather than any concern about pretence or deception, which forms the basis for the philosophical problem of other minds. Responses to this problem have tended to cluster around two solutions: either we know others’ minds through perception; or we know others’ minds through a form of inference. In the first part of this paper I argue that this debate is best understood as concerning the question of whether our knowledge of others’ minds is based on perception or based on evidence. In the second part of the paper I suggest that our ordinary ways of thinking take our knowledge of others’ minds to be both non- evidential and non-perceptual. A satisfactory resolution to the philosophical problem of other minds thus requires us to take seriously the idea that we have a way of knowing about others’ minds which is both non-evidential and non-perceptual. I suggest that our knowledge of others’ minds which is based on their expressions – our expressive knowledge - may fit this bill

Emblematic Arches – Contributions to Reading a Hapsburg Festival

In 1619 Philip III of Spain (II of Portugal) enters into Lisbon, in what was to be the culmination of a long awaited and extensively planned royal entrée into his Portuguese kingdom, in the context of the Iberian Dual Monarchy. Between the initial discussions for this journey nearly twenty years earlier and the journey itself, the political landscape of parts of remainder Hapsburg empire had changed, perchance none more so than in the religious and political schisms in the Low Countries, as evidenced in the Festival itself. The Lisbon festival featured various arches and ephemera, described and illustrated in Lavanha’s account (1622), and to which festival the ‘nação flamenga’ contributed with an arch. Lavanha’s account of this arch in particular simply provides a description of the arch and messages therein inscribed, in much the same way he does of the remainder events and ephemeral architecture. However, this particular arch sends a strong political message to Philip himself through applied devices which, when read in the context of their emblem book sources and their known readership in Portugal, Spain and, crucially, the Low Countries, reveal the full impact of the demand imposed on the king. In effect, the message conveyed by the arch goes well beyond the obvious Latin dedications translated by Lavanha. The interaction of the emblems with the Latin dedications and, crucially, with the mechanical apparatus of the arch, creates a strong and spectacular demand on the king, in which process he is, nonetheless, forced to participate. In effect, it will be the very own presence of the king that triggers the conclusion, thus publicly acquiescing to the demands of the Flemish in Lisbon. Our contribution addresses how the readership of a festival can be multisensory and multidirectional – to the public, to the addressee, to the dedicatee, and though mostly in static displays of ephemeral art, they convey political movement. However, the experience of the festival is also the stage for the redefinition of nationhood in 17th-century Habsburg Spain. Alongside trade guilds, whole nations performed in this public political arena to assert, defend and promote a unilateral concept of nationhood. Willingly or not, by reading together the various elements of the arch, crucially connected by emblems and mechanical contraptions, the king finds himself participating in a public display that commits him politically to resolve the schism of the Low Countries