Gauge Fixing in the Maxwell Like Gravitational Theory in Minkowski Spacetime and in the Equivalent Lorentzian Spacetime

In a previous paper we investigate a Lagrangian field theory for the gravitational field (which is there represented by a section g^a of the orthonormal coframe bundle over Minkowski spacetime. Such theory, under appropriate conditions, has been proved to be equivalent to a Lorentzian spacetime structure, where the metric tensor satisfies Einstein field equations. Here, we first recall that according to quantum field theory ideas gravitation is described by a Lagrangian theory of a possible massive graviton field (generated by matter fields and coupling also to itself) living in Minkowski spacetime. The graviton field is moreover supposed to be represented by a symmetric tensor field h carrying the representations of spin two and zero of the Lorentz group. Such a field, then (as it is well known), must necessarily satisfy the gauge condition given by Eq.(3) below. Next, we introduce an ansatz relating h to the 1-form fields g^a. Then, using the Clifford bundle formalism we derive, from our Lagrangian theory, the exact wave equation for the graviton and investigate the role of the gauge condition given by Eq.(3) in obtaining a reliable conservation law for the energy-momentum tensor of the gravitational plus the matter fields in Minkowski spacetime. Finally we ask the question: does Eq.(3) fix any gauge condition for the field g of the effective Lorentzian spacetime structure that represents the field h in our theory? We show that no gauge condition is fixed a priory, as is the case in General Relativity. Moreover we investigate under which conditions we may fix Logunov gauge condition.Comment: 15 pages. This version corrects some misprints of the published versio

Diffeomorphism Invariance and Local Lorentz Invariance

We show that diffeomorphism invariance of the Maxwell and the Dirac-Hestenes equations implies the equivalence among different universe models such that if one has a linear connection with non-null torsion and/or curvature the others have also. On the other hand local Lorentz invariance implies the surprising equivalence among different universe models that have in general different G-connections with different curvature and torsion tensors.Comment: 19 pages, Revtex, Plenary Talk presented at VII International Conference on Clifford Algebras and their Applications, Universite Paul Sabatier UFR MIG, Toulouse (FRANCE), to appear in "Clifford Algebras, Applications to Mathematics, Physics and Engineering", Progress in Math. Phys., Birkhauser, Berlin 200

The Einstein-Hilbert Lagrangian Density in a 2-dimensional Spacetime is an Exact Differential

Recently Kiriushcheva and Kuzmin claimed to have shown that the Einstein-Hilbert Lagrangian cannot be written in any coordinate gauge as an exact differential in a 2-dimensional spacetime. Since this is contrary to other statements on the subject found in the literature, as e.g., by Deser and Jackiw, Jackiw, Grumiller, Kummer and Vassilevich it is necessary to do decide who has reason. This is done in this paper in a very simply way using the Clifford bundle formalism. In this version we added Section 18 which discusses a recent comment on our paper just posted by Kiriushcheva and Kuzmin.Comment: 11 pages, Misprints in some equations have been corrected; four new references have been added, Section 18 adde

EDP and Naturgy : merger in utilities

When I chose the Mergers and Acquisitions (M&A) seminar for my thesis, I did so due to the internship I was attending at the time in a M&A department. There, I was allocated to the Technology, Media and Telecoms (TMT) and the Energy sectors, hence my choice. At the time, rumors started on a possible merger between Naturgy (ex-GNF) and EDP – Energias de Portugal, which didn’t amount to anything. My internship reached its end, but not my interest in the merger possibility and the sector. Throughout this thesis, I intend to learn if the merger would make sense for both sides, and which obstacles would Naturgy face if it had continued with their merger proposition. However, in May, China Three Gorges, a shareholder of EDP, decided to make an acquisition offer for the rest of the shares. This event added questions to my thesis: How did it affect EDP, and how would it influence a merger proposition from Naturgy? After a literature review on valuation and M&A, and an industry and company overview, I reached a valuation for both and a merger proposal, along with the respective analysis. I also give an insight on China Three Gorges’ offer.Quando escolhi o seminário de Mergers and Aquisitions (M&A) para fazer a minha tese, fi-lo porque me encontrava na altura a estagiar num departamento de M&A. Aqui estava alocado aos sectores de Tecnologia, Média e Telecomunicações (TMT) e de Energia, daí a minha escolha do sector energético. Durante o estágio, surgiram rumores de uma possível fusão entre a Naturgy (ex-GNF) e a EDP – Energias de Portugal, que acabou por não se concretizar. O estágio terminou mas o meu interesse na possibilidade da fusão e no sector não. Com esta tese, tenciono averiguar se esta fusão faria sentido para ambas as partes, e quais os obstáculos que a Naturgy iria encontrar se tivesse prosseguido com a proposta de fusão. Em Maio, no entanto, a China Three Gorges, accionista da EDP, decidiu fazer uma Oferta Pública de Aquisição (OPA) ao resto das acções que não possuía. Este evento acrescentou perguntas à minha tese: Como é que este evento afectou a EDP, e como influenciaria uma proposta de fusão por parte da Naturgy. Através de uma revisão da literatura existente sobre avaliação e M&A, análises do sector energético e das empresas mencionadas, chego a uma avaliação para cada uma e a propostas de fusões com as análises respectivas. Acabo também por dar um “insight” sobre a oferta da China Three Gorges

Assessing pension expenses determinants? The case of Portugal

Mestrado em Economia Monetária e FinanceiraA falta de estudos acerca do impacto de variáveis demográficas e económicas como o envelhecimento, produtividade e desemprego na despesa da Segurança Social Portuguesa promove o aparecimento de preocupações acerca da sua sustentabilidade financeira. Partindo de uma perspectiva teórica, a baixa fecundidade aumenta o índice de dependência de idosos e reduz o crescimento económico, com a agravante do desemprego que contrai a base contributiva e a produtividade (aumentando o peso da despesa com pensões na economia). No entanto, é crucial desenvolver um trabalho aplicado em Portugal nesta temática de modo a avaliar estas conclusões. Usando séries temporais de dados Portugueses de 1975 a 2014, foi encontrada evidência estatística de cointegração entre a população desempregada entre os 15 e os 64 anos de idade, produtividade aparente do trabalho e índice de dependência de idosos (variáveis explicativas) e despesa com pensões em percentagem do PIB (variável dependente), mas o sinal do coeficiente de longo prazo para a componente demográfica sofre alterações quando as variáveis dummy são excluídas , levantando dúvidas acerca do impacto do envelhecimento na despesa com pensões. As restantes variáveis explicativas apresentam um sinal positivo, influenciando positivamente a despesa com pensões em percentagem do PIB. Por ultimo, foi desenvolvido um modelo VECM com funções impulso-resposta e decomposição da variância, e os resultados evidenciam que, em Portugal, o envelhecimento tem um impacto quase insignificante no longo prazo, comparando com o desemprego e a produtividade.The lack of studies about the impact of demographic and economic variables such as ageing, productivity and unemployment, on Portuguese Social Security expenditures, arises expected concerns on its financial sustainability. From a theoretical perspective, low fertility increases old-age dependence index and decreases economic growth, reinforced by unemployment which shrinks the contributory base and productivity (increasing the burden of pension expenditures on the overall economy). However, it is crucial to develop an applied work in this field in Portugal to assess these conclusions. Using Portuguese time-series data from 1975 to 2014, it was found statistical evidence of cointegration between unemployed people aged between 15 and 64 years old, apparent productivity of labour and old-age dependence index (explanatory variables) and pension expenditure as a share of GDP (dependent variable), but the sign of long-run coefficient for the demographic component differs when the dummy components are excluded, raising doubts about the impact of ageing on pension expenditures. The remaining explanatory variables present a positive sign, positively influencing the pension expenditure as a share of GDP. At last, it was developed a VECM model with impulse-response functions and variance decomposition, and the results showed that, in Portugal, ageing has an almost insignificant impact in the long-run, comparing with unemployment and productivity.N/