Tricritical Ising Model near criticality

The most relevant thermal perturbation of the continuous d=2 minimal conformal theory with c=7/10 (Tricritical Ising Model) is treated here. This model describes the scaling region of the phi^6 universality class near the tricritical point. The problematic IR divergences of the naive perturbative expansion around conformal theories are dealt within the OPE approach developed at all orders by the authors. The main result is a description of the short distance behaviour of correlators that is compared with existing long distance expansion (form factors approach) related to the integrability of the model.Comment: LaTeX file, 15 pages +1 postscript figure included. Revised versio

Fermions in Instanton Anti-Instanton Background

We consider the behaviour of fermions in the background of instanton-anti\-instanton type configurations. Several different physics problems, from the high energy electroweak interactions to the study of vacuum structure of QCD and of large orders of perturbation theory are related to this problem. The spectrum of the Dirac operator in such a background is studied in detail. We present an approximation for the fermion correlation function when the instanton-anti\-instanton separation ($R$) is large compared to their sizes ($\rho$). The situation when the instanton-anti\-instanton overlap and melt, is studied through the behaviour of the Chern Simons number as a function of $R/\rho$ and $x_4$. Applying our results to widely discussed cases of fermion-number violation in the electroweak theory, we conclude that there are no theoretical basis for expecting anomalous cross sections to become observable at energies in $10$ TeV region.Comment: 36 PAGES, GEF-Th-8/199

Convergence of Scaled Delta Expansion: Anharmonic Oscillator

We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency $\Omega$ is chosen to scale with the order as $\Omega=CN^\gamma$; $1/30$ as $N\rightarrow\infty$. It converges also for $\gamma=1/3$, if $C\geq\alpha_c g^{1/3}$, $\alpha_c\simeq 0.570875$, where $g$ is the coupling constant in front of the operator $q^4/4$. The extreme case with $\gamma=1/3$, $C=\alpha_cg^{1/3}$ corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones.Comment: 37 pages (with 11 figures uuencoded at the end of the file,to be stripped off), GEF-Th-7/199

Improved Convergence Proof of the Delta Expansion and Order Dependent Mappings

We improve and generalize in several accounts the recent rigorous proof of convergence of delta expansion - order dependent mappings (variational perturbation expansion) for the energy eigenvalues of anharmonic oscillator. For the single-well anharmonic oscillator the uniformity of convergence in $g\in[0,\infty]$ is proven. The convergence proof is extended also to complex values of $g$ lying on a wide domain of the Riemann surface of $E(g)$. Via the scaling relation \`a la Symanzik, this proves the convergence of delta expansion for the double well in the strong coupling regime (where the standard perturbation series is non Borel summable), as well as for the complex ``energy eigenvalues'' in certain metastable potentials. Sufficient conditions for the convergence of delta expansion are summarized in the form of three theorems, which should apply to a wide class of quantum mechanical and higher dimensional field theoretic systems.Comment: some bugs of uuencoded postscript figures are fixe

Level-Crossing in the Instanton-Anti-Instanton Valley

We study the level crossing of the fermion system described by the euclidean Dirac Hamiltonian in the valley background. One chiral fermion level is shown to cross twice the zero value in the case of well-separated instanton-anti-instanton background. Below a critical separation, however, level crossings are absent. The phenomenon can be interpreted as the transition to a gauge field configuration of purely perturbative nature, below a critical instanton-anti-instanton separation. In the context of high-energy electroweak interactions, our findings seem to definitely invalidate some optimistic argument concerning the observability of baryon number violation based on the use of the optical theorem in conjunction with the valley fields.Comment: 12 Pages with one figure (PS) appended, GEF-Th-14/199

The study of the effect of glucocorticoids on global and tissue-specific metabolism in humans

Glucocorticoids are a class of steroid hormones which are highly relevant in human health and disease as they are involved in the regulation of carbohydrate, protein and fatty acid metabolism and are instrumental in the onset or progression of various diseases including those associated with glucocorticoid deficiency or excess. As an example, cortisol and insulin are involved in diurnal metabolic processes but their effects and interaction on healthy subjects are not completely elucidated yet. My PhD programme had the objectives to (1) assess and validate computational methodologies for application in untargeted metabolomic studies of healthy humans and those diagnosed with glucocorticoid-related diseases and (2) to investigate the global and tissue-specific metabolic changes induced by glucocorticoid excess and deficiency and their integrated effects with the relevant hormone insulin. A study of data pre-processing methods applied for untargeted metabolomics including different normalisation, missing value imputation, transformation and scaling methods were investigated on an in-silica modified dataset. The results showed that different combinations of data pre-processing methods influenced the results and different data pre-processing methods should be applied for univariate and multivariate analysis. Untargeted metabolomic studies ofbiotluids were applied to investigate in-vivo global effects of glucocorticoids. The study of the separate and integrated effects of cortisol and insulin showed that insulin may have negating effects on the influence of cortisol and treatment with cortisol should be timed appropriately during the day to minimize the effect of insulin on the therapeutic effect of cortisol. The studies reported here have shown the influence of the interactions between glucocorticoids and insulin across the metabolic network

Vacuum Expectation Values from a variational approach

In this letter we propose to use an extension of the variational approach known as Truncated Conformal Space to compute numerically the Vacuum Expectation Values of the operators of a conformal field theory perturbed by a relevant operator. As an example we estimate the VEV's of all (UV regular) primary operators of the Ising model and of some of the Tricritical Ising Model conformal field theories when perturbed by any choice of the relevant primary operators. We compare our results with some other independent predictions.Comment: LaTeX file, 11 pages. Revised Versio

Towards a fully automated computation of RG-functions for the 3-dd O(N) vector model: Parametrizing amplitudes

Within the framework of field-theoretical description of second-order phase transitions via the 3-dimensional O(N) vector model, accurate predictions for critical exponents can be obtained from (resummation of) the perturbative series of Renormalization-Group functions, which are in turn derived --following Parisi's approach-- from the expansions of appropriate field correlators evaluated at zero external momenta. Such a technique was fully exploited 30 years ago in two seminal works of Baker, Nickel, Green and Meiron, which lead to the knowledge of the $\beta$-function up to the 6-loop level; they succeeded in obtaining a precise numerical evaluation of all needed Feynman amplitudes in momentum space by lowering the dimensionalities of each integration with a cleverly arranged set of computational simplifications. In fact, extending this computation is not straightforward, due both to the factorial proliferation of relevant diagrams and the increasing dimensionality of their associated integrals; in any case, this task can be reasonably carried on only in the framework of an automated environment. On the road towards the creation of such an environment, we here show how a strategy closely inspired by that of Nickel and coworkers can be stated in algorithmic form, and successfully implemented on the computer. As an application, we plot the minimized distributions of residual integrations for the sets of diagrams needed to obtain RG-functions to the full 7-loop level; they represent a good evaluation of the computational effort which will be required to improve the currently available estimates of critical exponents.Comment: 54 pages, 17 figures and 4 table