(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev.

Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

We use the nonperturbative linear \delta expansion method to evaluate analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime} \ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where T_0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c_1 to order-\delta^2 with the result c_1= 3.06. Here, we push the calculation to the next two orders obtaining c_1=2.45 at order-\delta^3 and c_1=1.48 at order-\delta^4. Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.Comment: 29 pages, 3 eps figures. Minor changes, one reference added. Version in press Physical Review A (2002

Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem

We investigate the convergence properties of optimized perturbation theory, or linear $\delta$ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature T_c for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of $T_c$ in the large-N limit, when the relevant effective static action describing the system is extended to O(N) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for $T_c$ already at the first non-trivial order. Next, we consider the finite N=2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.Comment: 38 pages, 3 eps figures, Revtex4. Final version in press Phys. Rev.

A História da Alimentação: balizas historiográficas

Os M. pretenderam traçar um quadro da História da Alimentação, não como um novo ramo epistemológico da disciplina, mas como um campo em desenvolvimento de práticas e atividades especializadas, incluindo pesquisa, formação, publicações, associações, encontros acadêmicos, etc. Um breve relato das condições em que tal campo se assentou faz-se preceder de um panorama dos estudos de alimentação e temas correia tos, em geral, segundo cinco abardagens Ia biológica, a econômica, a social, a cultural e a filosófica!, assim como da identificação das contribuições mais relevantes da Antropologia, Arqueologia, Sociologia e Geografia. A fim de comentar a multiforme e volumosa bibliografia histórica, foi ela organizada segundo critérios morfológicos. A seguir, alguns tópicos importantes mereceram tratamento à parte: a fome, o alimento e o domínio religioso, as descobertas européias e a difusão mundial de alimentos, gosto e gastronomia. O artigo se encerra com um rápido balanço crítico da historiografia brasileira sobre o tema

Population genetic approaches to neurological disease: Parkinson's disease as an example

Parkinson's disease (PD) is a common, progressive, incurable disabling condition. The cause is unknown but over the past few years tremendous progress in our understanding of the genetic bases of this condition has been made. To date, this has almost exclusively come from the study of relatively rare Mendelian forms of the disease and there are no currently, widely accepted common variants known to increase susceptibility. The role that the ‘Mendelian’ genes play in common sporadic forms of PD is unknown. Moreover, most studies in PD can really be described as candidate polymorphism studies rather than true and complete assessments of the genes themselves. We provide a model of how one might tackle some of these issues using Parkinson's disease as an illustration. One of the emerging hypotheses of gene environment interaction in Parkinson's disease is based on drug metabolizing (or xenobiotic) enzymes and their interaction with putative environmental toxins. This motivated us to describe a tagging approach for an extensive but not exhaustive list of 55 drug metabolizing enzyme genes. We use these data to illustrate the power, and some of the limitations of a haplotype tagging approach. We show that haplotype tagging is extremely efficient and works well with only a modest increase in effort through different populations. The tagging approach works much less well if the minor allele frequency is below 5%. However, it will now be possible using these tags to evaluate these genes comprehensively in PD and other neurodegenerative conditions