Chiral Symmetry Breaking and Confinement Beyond Rainbow-Ladder Truncation

A non-perturbative construction of the 3-point fermion-boson vertex which obeys its Ward-Takahashi or Slavnov-Taylor identity, ensures the massless fermion and boson propagators transform according to their local gauge covariance relations, reproduces perturbation theory in the weak coupling regime and provides a gauge independent description for dynamical chiral symmetry breaking (DCSB) and confinement has been a long-standing goal in physically relevant gauge theories such as quantum electrodynamics (QED) and quantum chromodynamics (QCD). In this paper, we demonstrate that the same simple and practical form of the vertex can achieve these objectives not only in 4-dimensional quenched QED (qQED4) but also in its 3-dimensional counterpart (qQED3). Employing this convenient form of the vertex \emph{ansatz} into the Schwinger-Dyson equation (SDE) for the fermion propagator, we observe that it renders the critical coupling in qQED4 markedly gauge independent in contrast with the bare vertex and improves on the well-known Curtis-Pennington construction. Furthermore, our proposal yields gauge independent order parameters for confinement and DCSB in qQED3.Comment: 8 pages, 6 figure

Transverse Takahashi Identities and Their Implications for Gauge Independent Dynamical Chiral Symmetry Breaking

In this article, we employ transverse Takahashi identities to impose valuable non-perturbative constraints on the transverse part of the fermion-photon vertex in terms of new form factors, the so called $Y_i$ functions. We show that the implementation of these identities is crucial in ensuring the correct local gauge transformation of the fermion propagator and its multiplicative renormalizability. Our construction incorporates the correct symmetry properties of the $Y_i$ under charge conjugation operation as well as their well-known one-loop expansion in the asymptotic configuration of incoming and outgoing momenta. Furthermore, we make an explicit analysis of various existing constructions of this vertex against the demands of transverse Takahashi identities and the previously established key features of quantum electrodynamics, such as gauge invariance of the critical coupling above which chiral symmetry is dynamically broken. We construct a simple example in its quenched version and compute the mass function as we vary the coupling strength and also calculate the corresponding anomalous dimensions $\gamma_m$. There is an excellent fit to the Miransky scalling law and we find $\gamma_m=1$ rather naturally in accordance with some earlier results in literature, using arguments based on Cornwall-Jackiw-Tomboulis effective potential technique. Moreover, we numerically confirm the gauge invariance of this critical coupling.Comment: 16 pages, 4 figure

Climate change: causes, effects and the ways out

Climate is a significant and lasting change in the statistical distribution of weather pattern over periods ranging from decades to millions of years. It can be a change in average condition. Based on the broadest scale, the rate at which energy is received from the sun and the rate at which it is lost will determine the equilibrium temperature and climate of earth distributed around the globe by winds ocean currents and other mechanisms to affect the climate of different regions. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3603

Vacuum Polarization and Dynamical Chiral Symmetry Breaking: Phase Diagram of QED with Four-Fermion Contact Interaction

We study chiral symmetry breaking for fundamental charged fermions coupled electromagnetically to photons with the inclusion of four-fermion contact self-interaction term. We employ multiplicatively renormalizable models for the photon dressing function and the electron-photon vertex which minimally ensures mass anomalous dimension = 1. Vacuum polarization screens the interaction strength. Consequently, the pattern of dynamical mass generation for fermions is characterized by a critical number of massless fermion flavors above which chiral symmetry is restored. This effect is in diametrical opposition to the existence of criticality for the minimum interaction strength necessary to break chiral symmetry dynamically. The presence of virtual fermions dictates the nature of phase transition. Miransky scaling laws for the electromagnetic interaction strength and the four-fermion coupling, observed for quenched QED, are replaced by a mean-field power law behavior corresponding to a second order phase transition. These results are derived analytically by employing the bifurcation analysis, and are later confirmed numerically by solving the original non-linearized gap equation. A three dimensional critical surface is drawn to clearly depict the interplay of the relative strengths of interactions and number of flavors to separate the two phases. We also compute the beta-function and observe that it has ultraviolet fixed point. The power law part of the momentum dependence, describing the mass function, reproduces the quenched limit trivially. We also comment on the continuum limit and the triviality of QED.Comment: 9 pages, 10 figure

Ranolazine improves glucose and lipid homoestasis in streptozotocin induced diabetes mellitus in albino wistar rats

Background: Type 2 diabetes mellitus is one of the most common metabolic disorders at present with increasing incidence worldwide. The disease progresses with eventual multi-system involvement such as adverse cardiovascular outcomes. This necessitates pharmacotherapy which is able to retard disease progression, have a favourable cardiovascular profile in addition to stabilisation of glucose homeostasis. Ranolazine is an anti-anginal drug, which has been shown to reduce HbA1c in patients with CAD and diabetes in various clinical trials.Methods: Albino wistar rats of either sex weighing 150-200 grams, bred in central animal facility of JSS Medical College were used for the study. The animals were randomly divided into three groups of six animals each. Diabetes was induced in all 3 groups of animals by injecting streptozotocin in a dose of 45 mg/kg. After 72 hours of STZ administration, rats with blood glucose levels greater than 250 mg/dl were selected for the study. Capillary blood glucose levels were measured on 0, 7th, 14th, 21st, 28th days. Blood lipid levels were measured at baseline and day 28.Results: There was a persistent decrease in plasma glucose levels in the ranolazine treated animals during the study. Fasting plasma glucose levels were significantly lower in the ranolazine-treated group (206.3+12.74 mg/dl) compared with the vehicle group (437.8+34.03mg/dl) at 4 weeks. Ranolazine had a favourable effect on lipid profile when compared to the control (vehicle treated) animals.Conclusions: Ranolazine improved glucose and lipid homeostasis in streptozotocin induced diabetic wistar rats. Further studies are needed to validate the findings and elucidate the exact mechanism

Landau-Khalatnikov-Fradkin Transformations and the Fermion Propagator in Quantum Electrodynamics

We study the gauge covariance of the massive fermion propagator in three as well as four dimensional Quantum Electrodynamics (QED). Starting from its value at the lowest order in perturbation theory, we evaluate a non-perturbative expression for it by means of its Landau-Khalatnikov-Fradkin (LKF) transformation. We compare the perturbative expansion of our findings with the known one loop results and observe perfect agreement upto a gauge parameter independent term, a difference permitted by the structure of the LKF transformations.Comment: 9 pages, no figures, uses revte