Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model

We probe the U(N) Gross-Neveu model with a source-term $J\bar{\Psi}\Psi$. We find an expression for the renormalization scheme and scale invariant source $\hat{J}$, as a function of the generated mass gap. The expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter d. We get a non-perturbative mass gap as the solution of $\hat{J}=0$. In one loop we find that any physical choice for d gives good results for high values of N. In two loops we can determine d self-consistently by the principle of minimal sensitivity and find remarkably accurate results for N>2.Comment: 13 pages, 3 figures, added referenc

The mass gap and vacuum energy of the Gross-Neveu model via the 2PPI expansion

We introduce the 2PPI (2-point-particle-irreducible) expansion, which sums bubble graphs to all orders. We prove the renormalizibility of this summation. We use it on the Gross-Neveu model to calculate the mass gap and vacuum energy. After an optimization of the expansion, the final results are qualitatively good.Comment: 14 pages,19 eps figures, revtex

A Nonperturbative Study of Inverse Symmetry Breaking at High Temperatures

The optimized linear $\delta$-expansion is applied to multi-field $O(N_1) \times O(N_2)$ scalar theories at high temperatures. Using the imaginary time formalism the thermal masses are evaluated perturbatively up to order $\delta^2$ which considers consistently all two-loop contributions. A variational procedure associated with the method generates nonperturbative results which are used to search for parameters values for inverse symmetry breaking (or symmetry nonrestoration) at high temperatures. Our results are compared with the ones obtained by the one-loop perturbative approximation, the gap equation solutions and the renormalization group approach, showing good agreement with the latter method. Apart from strongly supporting inverse symmetry breaking (or symmetry nonrestoration), our results reveal the possibility of other high temperature symmetry breaking patterns for which the last term in the breaking sequence is $O(N_1-1) \times O(N_2-1)$.Comment: 28 pages,5 eps figures (uses epsf), RevTeX. Only a small misprint in Eq. (2.10) and a couple of typos fixe

On the Divergence of Perturbation Theory. Steps Towards a Convergent Series

The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of the Dominated Convergence Theorem of Lebesgue using familiar techniques of Quantum Field Theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.Comment: 42 pages, Latex, 4 figure

(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.

Variational Quark Mass Expansion and the Order Parameters of Chiral Symmetry Breaking

We investigate in some detail a "variational mass" expansion approach, generalized from a similar construction developed in the Gross-Neveu model, to evaluate the basic order parameters of the dynamical breaking of the $SU(2)_L \times SU(2)_R$ and $SU(3)_L \times SU(3)_R$ chiral symmetries in QCD. The method starts with a reorganization of the ordinary perturbation theory with the addition of an arbitrary quark mass $m$. The new perturbative series can be summed to all orders thanks to renormalization group properties, with specific boundary conditions, and advocated analytic continuation in $m$ properties. In the approximation where the explicit breakdown of the chiral symmetries due to small current quark masses is neglected, we derive ansatzes for the dynamical contribution to the "constituent" masses $M_q$ of the $u,d,s$ quarks; the pion decay constant $F_\pi$; and the quark condensate $$ in terms of the basic QCD scale $\Lambda_{\bar{MS}}$. Those ansatzes are then optimized, in a sense to be specified, and also explicit symmetry breaking mass terms can be consistently introduced in the framework. The obtained values of $F_\pi$ and $M_q$ are roughly in agreement with what is expected from other non-perturbative methods. In contrast we obtain quite a small value of $|< \bar q q >|$ within our approach. The possible interpretation of the latter results is briefly discussed.Comment: 40 pages, LaTex, 2 PS figures. Additions in section 2.2 to better explain the relation between the current mass and the dynamical mass ansatz. Minor misprints corrected. Version to appear in Phys. Rev.

Four-Dimensional Computational Ultrasound Imaging of Brain Haemodynamics

Four-dimensional ultrasound imaging of complex biological systems such as the brain is technically challenging because of the spatiotemporal sampling requirements. We present computational ultrasound imaging (cUSi), a new imaging method that uses complex ultrasound fields that can be generated with simple hardware and a physical wave prediction model to alleviate the sampling constraints. cUSi allows for high-resolution four-dimensional imaging of brain haemodynamics in awake and anesthetized mice

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

Harmonising evidence-based medicine teaching: a study of the outcomes of e-learning in five European countries

BACKGROUND: We developed and evaluated the outcomes of an e-learning course for evidence based medicine (EBM) training in postgraduate medical education in different languages and settings across five European countries. METHODS: We measured changes in knowledge and attitudes with well-developed assessment tools before and after administration of the course. The course consisted of five e-learning modules covering acquisition (formulating a question and search of the literature), appraisal, application and implementation of findings from systematic reviews of therapeutic interventions, each with interactive audio-visual learning materials of 15 to 20 minutes duration. The modules were prepared in English, Spanish, German and Hungarian. The course was delivered to 101 students from different specialties in Germany (psychiatrists), Hungary (mixture of specialties), Spain (general medical practitioners), Switzerland (obstetricians-gynaecologists) and the UK (obstetricians-gynaecologists). We analysed changes in scores across modules and countries. RESULTS: On average across all countries, knowledge scores significantly improved from pre- to post-course for all five modules (p < 0.001). The improvements in scores were on average 1.87 points (14% of total score) for module 1, 1.81 points (26% of total score) for module 2, 1.9 points (11% of total score) for module 3, 1.9 points (12% of total score) for module 4 and 1.14 points (14% of total score) for module 5. In the country specific analysis, knowledge gain was not significant for module 4 in Spain, Switzerland and the UK, for module 3 in Spain and Switzerland and for module 2 in Spain. Compared to pre-course assessment, after completing the course participants felt more confident that they can assess research evidence and that the healthcare system in their country should have its own programme of research about clinical effectiveness. CONCLUSION: E-learning in EBM can be harmonised for effective teaching and learning in different languages, educational settings and clinical specialties, paving the way for development of an international e-EBM course

Convergent resummed linear delta expansion in the critical O(N) (\phi_i^2)^2_{3d} model

The nonperturbative linear delta expansion (LDE) method is applied to the critical O(N) phi^4 three-dimensional field theory which has been widely used to study the critical temperature of condensation of dilute weakly interacting homogeneous Bose gases. We study the higher order convergence of the LDE as it is usually applied to this problem. We show how to improve both, the large-N and finite N=2, LDE results with an efficient resummation technique which accelerates convergence. In the large N limit, it reproduces the known exact result within numerical integration accuracy. In the finite N=2 case, our improved results support the recent numerical Monte Carlo estimates for the critical transition temperature of Bose-Einstein condensation.Comment: 4 pages, Revtex 4. A misprint in Eq. (3) was corrected and ref. 17 (cond-mat/0207295) update