Momentum Space Regularizations and the Indeterminacy in the Schwinger Model

We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an {\it ansatz} in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and their violations are discussed. The analysis is carried out in both analytical and sharp cutoff regularization procedures. We also show how the Pauli Villars regularization scheme eliminates the indeterminacy, giving a gauge invariant result in the vector Schwinger model.Comment: 10 pages, no figure

Phase Transition and Monopoles Densities in a Nearest Neighbors Two-Dimensional Spin Ice Model

In this work, we show that, due to the alternating orientation of the spins in the ground state of the artificial square spin ice, the influence of a set of spins at a certain distance of a reference spin decreases faster than the expected result for the long range dipolar interaction, justifying the use of the nearest neighbor two dimensional square spin ice model as an effective model. Using an extension of the model presented in ref. [Scientific Reports 5, 15875 (2015)], considering the influence of the eight nearest neighbors of each spin on the lattice, we analyze the thermodynamics of the model and study the monopoles and string densities dependence as a function of the temperature.Comment: 11 pages, 8 figure

Spin g-factor due to electronic interactions in graphene

The gyromagnetic factor is an important physical quantity relating the magnetic-dipole moment of a particle to its spin. The electron spin g-factor in vacuo is one of the best model-based theoretical predictions ever made, showing agreement with the measured value up to ten parts per trillion. However, for electrons in a material the g-factor is modified with respect to its value in vacuo because of environment interactions. Here, we show how interaction effects lead to the spin g-factor correction in graphene by considering the full electromagnetic interaction in the framework of pseudo-QED. We compare our theoretical prediction with experiments performed on graphene deposited on SiO2 and SiC, and we find a very good agreement between them.Comment: Improved version of the manuscript; valley g-factor part has been remove

de Broglie-Proca and Bopp-Podolsky massive photon gases in cosmology

We investigate the influence of massive photons on the evolution of the expanding universe. Two particular models for generalized electrodynamics are considered, namely de Broglie-Proca and Bopp-Podolsky electrodynamics. We obtain the equation of state (EOS) $P=P(\varepsilon)$ for each case using dispersion relations derived from both theories. The EOS are inputted into the Friedmann equations of a homogeneous and isotropic space-time to determine the cosmic scale factor $a(t)$. It is shown that the photon non-null mass does not significantly alter the result $a\propto t^{1/2}$ valid for a massless photon gas; this is true either in de Broglie-Proca's case (where the photon mass $m$ is extremely small) or in Bopp-Podolsky theory (for which $m$ is extremely large).Comment: 8 pages, 2 figures; v2 matches the published versio

Phase Transition in Asymmetrical Superfluids I: Equal Fermi Surfaces

In this paper, we study phase transitions in asymmetrical fermion superfluids. In this scenario, the candidates to form pair are particles with mismatched masses and chemical potentials. We derive an expression for the critical temperature in terms of the gap and masses (or chemical potentials) when the constraint of equal Fermi surfaces $m_a\mu_a = m_b\mu_b$ is imposed.Comment: RevTex, 11 pages, 2 figures, typos corrected and an appendix added, accepted for publication in Phys. Rev.

Meningites - estudo descritivo de uma população pediátrica do norte e centro de Portugal

Objectivos: Caracterizar os casos de meningite quanto à sua etiologia, tratamento e evolução. Doentes e Métodos: Estudo multicêntrico, descritivo, retrospectivo (1 de Janeiro de 2000 a 28 de Fevereiro de 2003) e prospectivo (1 de Março a 31 de Julho de 2003) dos casos de meningite ocorridos em crianças com idades compreendidas entre 1 mês e 10 anos, inclusive. Resultados: Participaram neste estudo 17 hospitais das zonas norte e centro de Portugal. Foram incluídos 876 casos (802 do ramo retrospectivo). Registaram-se 110 casos de meningite bacteriana e 111 de meningite vírica (sendo as restantes assépticas ou decapitadas). O agente mais frequente de meningite bacteriana foi o meningococo seguido pelo pneumococo. A generalidade dos casos foi medicada com uma cefalosporina de 3ª geração isoladamente, verificando-se um elevado nº de crianças tratadas com dexametasona (62%) e restrição hídrica (36%). Registaram- se 18 casos de complicações agudas, 2 óbitos e sequelas permanentes em 8 crianças. Em todos as meningites víricas foi identificado um enterovírus. Foram detectadas diferenças estatisticamente significativas (p<0,05) entre estes dois grupos (víricas vs bacterianas) em relação à idade (<5 e ≥5 anos) à febre (< 39,5 e ≥ 39,5ºC) e aos parâmetros laboratoriais (contagem de leucócitos e neutrófilos no sangue, PCR, contagem de leucócitos e neutrófilos no LCR e proteinorráquia). Conclusões: A epidemiologia dos casos esteve de acordo com o esperado, bem como a escolha da terapêutica empírica e a evolução. Em relação à terapêutica adjuvante, a utilização de dexametasona e o recurso à restrição hídrica deverão ser repensadas

On the intrinsic complexity of the arithmetic Nullstellensatz

We show several arithmetic estimates for Hilbert's Nullstellensatz. This includes an algorithmic procedure computing the polynomials and constants occurring in a Bézout identity, whose complexity is polynomial in the geometric degree of the system. Moreover, we show for the first time height estimates of intrinsic type for the polynomials and constants appearing, again polynomial in the geometric degree and linear in the height of the system. These results are based on a suitable representation of polynomials by straight-line programs and duality techniques using the Trace Formula for Gorenstein algebras. As an application we show more precise upper bounds for the function πS(x) counting the number of primes yielding an inconsistent modular polynomial equation system. We also give a computationally interesting lower bound for the density of small prime numbers of controlled bit length for the reduction to positive characteristic of inconsistent systems. Again, this bound is given in terms of intrinsic parameters.Facultad de Ciencias Exacta

On the intrinsic complexity of the arithmetic Nullstellensatz

We show several arithmetic estimates for Hilbert's Nullstellensatz. This includes an algorithmic procedure computing the polynomials and constants occurring in a Bézout identity, whose complexity is polynomial in the geometric degree of the system. Moreover, we show for the first time height estimates of intrinsic type for the polynomials and constants appearing, again polynomial in the geometric degree and linear in the height of the system. These results are based on a suitable representation of polynomials by straight-line programs and duality techniques using the Trace Formula for Gorenstein algebras. As an application we show more precise upper bounds for the function πS(x) counting the number of primes yielding an inconsistent modular polynomial equation system. We also give a computationally interesting lower bound for the density of small prime numbers of controlled bit length for the reduction to positive characteristic of inconsistent systems. Again, this bound is given in terms of intrinsic parameters.Facultad de Ciencias Exacta