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

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

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

The nonperturbative propagator and vertex in massless quenched QED_d

It is well known how multiplicative renormalizability of the fermion propagator, through its Schwinger-Dyson equation, imposes restrictions on the 3-point fermion-boson vertex in massless quenched quantum electrodynamics in 4-dimensions (QED$_4$). Moreover, perturbation theory serves as an excellent guide for possible nonperturbative constructions of Green functions. We extend these ideas to arbitrary dimensions $d$. The constraint of multiplicative renormalizability of the fermion propagator is generalized to a Landau-Khalatnikov-Fradkin transformation law in $d$-dimensions and it naturally leads to a constraint on the fermion-boson vertex. We verify that this constraint is satisfied in perturbation theory at the one loop level in 3-dimensions. Based upon one loop perturbative calculation of the vertex, we find additional restrictions on its possible nonperturbative forms in arbitrary dimensions.Comment: 13 pages, no figures, latex (uses IOP style files

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

Adaptive sampling in context-aware systems: a machine learning approach

As computing systems become ever more pervasive, there is an increasing need for them to understand and adapt to the state of the environment around them: that is, their context. This understanding comes with considerable reliance on a range of sensors. However, portable devices are also very constrained in terms of power, and hence the amount of sensing must be minimised. In this paper, we present a machine learning architecture for context awareness which is designed to balance the sampling rates (and hence energy consumption) of individual sensors with the significance of the input from that sensor. This significance is based on predictions of the likely next context. The architecture is implemented using a selected range of user contexts from a collected data set. Simulation results show reliable context identification results. The proposed architecture is shown to significantly reduce the energy requirements of the sensors with minimal loss of accuracy in context identification