Vacuum Stability of the PT\mathcal{PT}-Symmetric (−ϕ4)\left( -\phi^{4}\right) Scalar Field Theory

In this work, we study the vacuum stability of the classical unstable $\left( -\phi^{4}\right)$ scalar field potential. Regarding this, we obtained the effective potential, up to second order in the coupling, for the theory in $1+1$ and $2+1$ space-time dimensions. We found that the obtained effective potential is bounded from below, which proves the vacuum stability of the theory in space-time dimensions higher than the previously studied $0+1$ case. In our calculations, we used the canonical quantization regime in which one deals with operators rather than classical functions used in the path integral formulation. Therefore, the non-Hermiticity of the effective field theory is obvious. Moreover, the method we employ implements the canonical equal-time commutation relations and the Heisenberg picture for the operators. Thus, the metric operator is implemented in the calculations of the transition amplitudes. Accordingly, the method avoids the very complicated calculations needed in other methods for the metric operator. To test the accuracy of our results, we obtained the exponential behavior of the vacuum condensate for small coupling values, which has been obtained in the literature using other methods. We assert that this work is interesting, as all the studies in the literature advocate the stability of the $\left( -\phi^{4}\right)$ theory at the quantum mechanical level while our work extends the argument to the level of field quantization.Comment: 20 pages, 4 figures, appendix added and more details have been added to

Effective Field calculations of the Energy Spectrum of the PT\mathcal{PT}% -Symmetric (−x4-x^{4}) Potential

In this work, we show that the traditional effective field approach can be applied to the $\mathcal{PT}$-symmetric wrong sign ($-x^{4}$) quartic potential. The importance of this work lies in the possibility of its extension to the more important $\mathcal{PT}$-symmetric quantum field theory while the other approaches which use complex contours are not willing to be applicable. We calculated the effective potential of the massless $-x^{4}$ theory as well as the full spectrum of the theory. Although the calculations are carried out up to first order in the coupling, the predicted spectrum is very close to the exact one taken from other works. The most important result of this work is that the effective potential obtained, which is equivalent to the Gaussian effective potential, is bounded from below while the classical potential is bounded from above. This explains the stability of the vacuum of the theory. The obtained quasi-particle Hamiltonian is non-Hermitian but $\mathcal{PT}$-symmetric and we showed that the calculation of the metric operator can go perturbatively. In fact, the calculation of the metric operator can be done even for higher dimensions (quantum field theory) which, up till now, can not be calculated in the other approaches either perturbatively or in a closed form due to the possible appearance of field radicals. Moreover, we argued that the effective theory is perturbative for the whole range of the coupling constant and the perturbation series is expected to converge rapidly (the effective coupling $g_{eff}={1/6}$).Comment: 14 pages, 5 figure

Representation Dependence of Superficial Degree of Divergences in Quantum Field Theory

In this work, we investigate a very important but unstressed result in the work of Carl M. Bender, Jun-Hua Chen, and Kimball A. Milton ( J.Phys.A39:1657-1668, 2006). In this article, Bender \textit{et.al} have calculated the vacuum energy of the $i\phi^{3}$ scalar field theory and its Hermitian equivalent theory up to $g^{4}$ order of calculations. While all the Feynman diagrams of the $i\phi^{3}$ theory are finite in $0+1$ space-time dimensions, some of the corresponding Feynman diagrams in the equivalent Hermitian theory are divergent. In this work, we show that the divergences in the Hermitian theory originate from superrenormalizable, renormalizable and non-renormalizable terms in the interaction Hamiltonian even though the calculations are carried out in the $0+1$ space-time dimensions. Relying on this interesting result, we raise the question, is the superficial degree of divergence of a theory is representation dependent? To answer this question, we introduce and study a class of non-Hermitian quantum field theories characterized by a field derivative interaction Hamiltonian. We showed that the class is physically acceptable by finding the corresponding class of metric operators in a closed form. We realized that the obtained equivalent Hermitian and the introduced non-Hermitian representations have coupling constants of different mass dimensions which may be considered as a clue for the possibility of considering non-Renormalizability of a field theory as a non-genuine problem. Besides, the metric operator is supposed to disappear from path integral calculations which means that physical amplitudes can be fully obtained in the simpler non-Hermitian representation.Comment: 14 pages one figure. The title has been change

The type II phase resetting curve is optimal for stochastic synchrony

The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized. However, the inputs to real neurons may often be more accurately described as barrages of synaptic noise. Effective connectivity between cells may thus arise in the form of correlations between the noisy input streams. We use constrained optimization and perturbation methods to prove that PRC shape determines susceptibility to synchrony among otherwise uncoupled noise-driven neural oscillators. PRCs can be placed into two general categories: Type I PRCs are non-negative while Type II PRCs have a large negative region. Here we show that oscillators with Type II PRCs receiving common noisy input sychronize more readily than those with Type I PRCs.Comment: 10 pages, 4 figures, submitted to Physical Review

A Novel phase in the phase structure of the (gϕ4+hϕ6)1+1(g\phi^4 + h\phi^6)_{1+1} field theoretic model

In view of the newly discovered and physically acceptable $PT$ symmetric and non-Hermitian models, we reinvestigated the phase structure of the ($g\phi^{4}+h\phi^{6}$)$_{1+1}$ Hermitian model. The reinvestigation concerns the possibility of a phase transition from the original Hermitian and $PT$ symmetric phase to a non-Hermitian and $PT$ symmetric one. This kind of phase transition, if verified experimentally, will lead to the first proof that non-Hermitian and $PT$ symmetric models are not just a mathematical research framework but are a nature desire. To do the investigation, we calculated the effective potential up to second order in the couplings and found a Hermitian to Non-Hermitian phase transition. This leads us to introduce, for the first time, hermiticity as a symmetry which can be broken due to quantum corrections, \textit{i.e.}, when starting with a model which is Hermitian in the classical level, quantum corrections can break hermiticity while the theory stays physically acceptable. In fact, ignoring this phase will lead to violation of universality when comparing this model predictions with other models in the same class of universality. For instance, in a previous work we obtained a second order phase transition for the $PT$ symmetric and non-Hermitian $(-g\phi^{4})$ and according to universality, this phase should exist in the phase structure of the ($g\phi^{4}+h\phi^{6}$) model for negative $g$. Finally, among the novelties in this letter, in our calculation for the effective potential, we introduced a new renormalization group equation which describes the invariance of the bare vacuum energy under the change of the scale. We showed that without this invariance, the original theory and the effective one are inequivalent.Comment: 13 pages, 4 figure

A population-based observational study of diabetes during pregnancy in Victoria, Australia, 1999-2008

Objectives: This paper reports secular trends in diabetes in pregnancy in Victoria, Australia and examines the effect of including or excluding women with pre-existing diabetes on gestational diabetes (GDM) prevalence estimates

Correlation transfer in stochastically driven oscillators over long and short time scales

In the absence of synaptic coupling, two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams. Recent work has shown that the degree of correlation transfer from input currents to output spikes depends not only on intrinsic oscillator dynamics, but also depends on the length of the observation window over which the correlation is calculated. In this paper we use stochastic phase reduction and regular perturbations to derive the correlation of the total phase elapsed over long time scales, a quantity which provides a convenient proxy for the spike count correlation. Over short time scales, we derive the spike count correlation directly using straightforward probabilistic reasoning applied to the density of the phase difference. Our approximations show that output correlation scales with the autocorrelation of the phase resetting curve over long time scales. We also find a concise expression for the influence of the shape of the phase resetting curve on the initial slope of the output correlation over short time scales. These analytic results together with numerical simulations provide new intuitions for the recent counterintuitive finding that type I oscillators transfer correlations more faithfully than do type II over long time scales, while the reverse holds true for the better understood case of short time scales.Comment: 9 pages, 7 figures, submitted to Physical Review

An effective scalable SQL engine for NoSQL databases

NoSQL databases were initially devised to support a few concrete extreme scale applications. Since the specificity and scale of the target systems justified the investment of manually crafting application code their limited query and indexing capabilities were not a major im- pediment. However, with a considerable number of mature alternatives now available there is an increasing willingness to use NoSQL databases in a wider and more diverse spectrum of applications and, to most of them, hand-crafted query code is not an enticing trade-off. In this paper we address this shortcoming of current NoSQL databases with an effective approach for executing SQL queries while preserving their scalability and schema flexibility. We show how a full-fledged SQL engine can be integrated atop of HBase leading to an ANSI SQL compli- ant database. Under a standard TPC-C workload our prototype scales linearly with the number of nodes in the system and outperforms a NoSQL TPC-C implementation optimized for HBase.(undefined

Interactions between learner’s beliefs, behaviour and environment in online learning: Path analysis

Introduction: Although, several factors have been identified as significant determinants in online learning, the human interactions with those factors and their effect on academic achievement are not fully elucidated. This study aims to determine the effect of self-regulated learning (SRL) on achievement in online learning through exploring the relations and interaction of the conception of learning, online discussion, and the e-learning experience. Methods: A non-probability convenience sample of 128 learners in the Health Professions Education program through online learning filled-out three self-reported questionnaires to assess SRL strategies, the conception of learning, the quality of e-Learning experience and online discussion. A scoring rubric was used to assess the online discussion contributions. A path analysis model was developed to examine the effect of self-regulated learning on achievement in online learning through exploring the relations and interaction among the other factors. Results: Path analysis showed that SRL has a statistically significant relationship with the quality of e-learning experience, and the conception of learning. On the other hand, there was no correlation with academic achievement and online discussion. However, academic achievement did show a correlation with online discussion. Conclusion: The study showed a dynamic interaction between the students’ beliefs and the surrounding environment that can significantly and directly affect their behaviour in online learning. Moreover, online discussion is an essential activity in online learning

Standardizing clinical care measures of rheumatic heart disease in pregnancy: A qualitative synthesis

© 2019 Wiley Periodicals, Inc. Background: Rheumatic heart disease (RHD) is a preventable cardiac condition that escalates risk in pregnancy. Models of care informed by evidence-based clinical guidelines are essential to optimal health outcomes. There are no published reviews that systematically explore approaches to care provision for pregnant women with RHD and examine reported measures. The review objective was to improve understanding of how attributes of care for these women are reported and how they align with guidelines. Methods: A search of 13 databases was supported by hand-searching. Papers that met inclusion criteria were appraised using CASP/JBI checklists. A content analysis of extracted data from the findings sections of included papers was undertaken, informed by attributes of quality care identified previously from existing guidelines. Results: The 43 included studies were predominantly conducted in tertiary care centers of low-income and middle-income countries. Cardiac guidelines were referred to in 25 of 43 studies. Poorer outcomes were associated with higher risk scores (detailed in 36 of 41 quantitative studies). Indicators associated with increased risk include anticoagulation during pregnancy (28 of 41 reported) and late booking (gestation documented in 15 of 41 studies). Limited access to cardiac interventions was discussed (19 of 43) in the context of poorer outcomes. Conversely, early assessment and access to regular multidisciplinary care were emphasized in promoting optimal outcomes for women and their babies. Conclusions: Despite often complex care requirements in challenging environments, pregnancy provides an opportunity to strengthen health system responses and address whole-of-life health for women with RHD. A standard set of core indicators is proposed to more accurately benchmark care pathways, outcomes, and burden