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

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

Gauge Theory in Riem(M)

In the geometrodynamical setting of general relativity in Lagrangian form, the objects of study are the {\it Riemannian} metrics (and their time derivatives) over a given 3-manifold $M$. It is our aim in this paper to study the gauge properties that the space Riem(M) of all metrics over $M$ possesses, specially as they relate to the constraints of geometrodynamics. For instance, the Hamiltonian constraint does not generate a group, and it is thus hard to view its action in Riem(M) in a gauge setting. However, in view of the recent results representing GR as a dual theory, invariant under foliation preserving 3--diffeomorphisms and 3D conformal transformations, but not under refoliations, we are justified in considering the gauge structure pertaining only to the groups $\mathcal{D}$ of diffeomorphisms of $M$, and $\mathcal{C}$, of conformal diffeomorphisms on $M$. For these infinite-dimensional symmetry groups, Riem(M) has a natural principal fiber bundle (PFB) structure, which renders the gravitational field amenable to the full range of gauge-theoretic treatment. We discuss some of these structures and construct explicit formulae for supermetric-induced gauge connections. To apply the formalism, we compute general properties for a specific connection bearing strong resemblance to the one naturally induced by the deWitt supermetric, showing it has desirable relationalist properties. Finally, we find that the group of conformal diffeomorphisms solves the pathologies inherent in the \DD group and also brings it closer to Horava gravity and the dual conformal theory called Shape Dynamics.Comment: Version virtually identical to the one published in J. Math. Phys. Contains corrections to a crucial proof, and new figure

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