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

Dyonic Integrable Models

A class of non abelian affine Toda models arising from the axial gauged two-loop WZW model is presented. Their zero curvature representation is constructed in terms of a graded Kac-Moody algebra. It is shown that the discrete multivacua structure of the potential together with non abelian nature of the zero grade subalgebra allows soliton solutions with non trivial electric and topological charges. The dressing transformation is employed to explicitly construct one and two soliton solutions and their bound states in terms of the tau functions. A discussion of the classical spectra of such solutions and the time delays are given in detail.Comment: Latex 30 pages, corrected some typo

Conservation laws arising in the study of forward-forward Mean-Field Games

We consider forward-forward Mean Field Game (MFG) models that arise in numerical approximations of stationary MFGs. First, we establish a link between these models and a class of hyperbolic conservation laws as well as certain nonlinear wave equations. Second, we investigate existence and long-time behavior of solutions for such models

Free will, the self and the brain

The free will problem is defined and three solutions are discussed: no-freedom theory, libertarianism, and compatibilism. Strict determinism is often assumed in arguing for libertarianism or no-freedom theory. It assumes that the history of the universe is fixed, but modern physics admits a certain degree of randomness in the determination of events. However, this is not enough for a compatibilist position—which is favored here—since freedom is not randomness. It is the I that chooses what to do. It is argued that the core of the free will problem is what this I is. A materialist view is favored: The I is an activity of the brain. In addition to absence of external and internal compulsion, freedom involves absence of causal sufficiency of influences acting on the I. A more elaborate compatibilist view is proposed, according to which causal determination is complete when we add events occurring in the I (of which the subject is not conscious). Contrary to what several authors have argued, the onset of the readiness potential before the decision to act is no problem here. The experience of agency is incomplete and fallible, rather than illusory. Some consequences of different views about freedom for the ascription of responsibility are discussed

A two-dimensional non-equilibrium dynamic model

This paper develops a non-equilibrium dynamic model (NEDyM) with Keynesian features (it allows for a disequilibrium between output and demand and it considers a constant marginal propensity to consume), but where production is undertaken under plain neoclassical conditions (a constant returns to scale production function, with the stocks of capital and labor fully employed, is assumed). The model involves only two endogenous / prognostic variables: the stock of physical capital per unit of labor and a goods inventory measure. The two-dimensional system allows for a careful analysis of local and global dynamics. Points of bifurcation and long-term cyclical motion are identified. The main conclusion is that the disequilibrium hypothesis leads to persistent fluctuations generated by intrinsic deterministic factors

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

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