The description of gravitational waves in geometric scalar gravity

It is investigated the gravitational waves phenomena in the geometric scalar theory of gravity (GSG), a class of theories such that gravity is described by a single scalar field. The associated physical metric describing the spacetime is constructed from a disformal transformation of Minkowski geometry. In this theory, a weak field approximation gives rise to a description similar to that one obtained in general relativity, with the gravitational waves propagating at the same speed as the light, although they have a characteristic longitudinal polarization mode, besides others modes that are observer dependent. We also analyze the energy carried by the gravitational waves as well as how their emission affects the orbital period of a binary system. Observational data coming from Hulse and Taylor binary pulsar is then used to constraint the theory parameter.Comment: Revised version accepted for publication in EPJC; confrontation with pulsar observational data added; abstract slightly changed. arXiv admin note: substantial text overlap with arXiv:1607.0103

Free structures in division rings

Makar-Limanov's conjecture states that if a division ring D is finitely generated and infinite dimensional over its center k then D contains a free k-subalgebra of rank 2. In this work, we will investigate the existence of such structures in D, the division ring of fractions of the skew polynomial ring L[t;\sigma], where t is a variable and $\sigma$ is a k-automorphism of L. For instance, we prove Makar-Limanov's conjecture when either L is the function field of an abelian variety or the function field of the n-dimensional projective space.Comment: 12 page

Complex-mass shell renormalization of the higher-derivative electrodynamics

We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron--positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed.Comment: 10 pages, 2 figures, replaced with published versio

Cities: Continuity, transformation and emergence

Book synopsis: This book applies ideas and methods from the complexity perspective to key concerns in the social sciences, exploring co-evolutionary processes that have not yet been addressed in the technical or popular literature on complexity. \ud \ud Authorities in a variety of fields – including evolutionary economics, innovation and regeneration studies, urban modelling and history – re-evaluate their disciplines within this framework. The book explores the complex dynamic processes that give rise to socio-economic change over space and time, with reference to empirical cases including the emergence of knowledge-intensive industries and decline of mature regions, the operation of innovative networks and the evolution of localities and cities. Sustainability is a persistent theme and the practicability of intervention is examined in the light of these perspectives. \ud \ud Specialists in disciplines that include economics, evolutionary theory, innovation, industrial manufacturing, technology change, and archaeology will find much to interest them in this book. In addition, the strong interdisciplinary emphasis of the book will attract a non-specialist audience interested in keeping abreast of current theoretical and methodological approaches through evidence-based and practical examples