Constructing vertices in QED

We study the Dyson Schwinger Equation for the fermion propagator in the quenched approximation. We construct a non-preservative fermion-boson vertex that ensures the fermion propagator satisfies the Ward-Takahashi identity, is multiplicatively renormalizable, agrees with the lowest order perturbation theory for weak couplings and has a critical coupling for dynamical mass generation that is strictly gauge independent. This is in marked contrast to the rainbow approximation in which the critical coupling changes by 50% just between the Landau and Feynman gauges. We also show how to construct a vertex which not only has the aforementioned properties but also agrees with the results obtained from the CJT effective potential for the critical exponent of the mass function. These vertices are expressed in terms of two functions which satisfy an integral and a derivative condition. By considering the perturbative expansion for the transverse vertex, we have performed numerical evaluation of the first of these functions which will hopefully guide their non-perturbative structure. The use of vertices satisfying these properties should lead to a more believable study of mass generation

IMPACT OF CUSTOMER BRAND RELATIONSHIP THROUGH FACEBOOK ON THE LEVEL OF CUSTOMER ENGAGEMENT

In the last few years customer engagement has received asignificant attention of researchers and marketers’ because there is arise in the awareness of customers as value recipient to value cocreator.Two hypotheses were developed i.e. 1) Customer BrandRelationship through facebook impacts on the level of customerengagement. 2) There is a gender difference on the variable ofcustomer engagement on facebook. A survey was designed by takingten different brands of cloths that have their web pages on onlinesocial media. A sample of 211 individuals was approached to measurethe engagement status of 10 clothing brands through online socialmedia. Customer Engagement Scale (CES; Justina Malciute, 2012)was used to measure the impact of customer brand relationshipthrough Facebook on the level of Customer Engagement. Regressionanalysis was performed to measure the results. The results of thestudy suggest that customer brand relationship through facebookwill impact the level of customer engagement. Moreover, no genderdifference was found on the variable of customer engagement onfacebook

The Economies of Scale and Efficiency of Small-Scale Capture Fisheries in Kurau Village, Central Bangka District

This study investigates the economies of scale and efficiency of small-scale capture fisheries, as well as to know how the socio-economic variable influencing the small-scale capture fisheries business in the Kurau village, Central Bangka district. The approach used is a quantitative method by applying multiple linear regression models to adopt the Cobb-Douglas production function. The study found that the scale-economies condition in the small-scale fisheries is decreasing return to scale. We also found the results of allocative efficiency in this small-scale fisheries business are relatively inefficient. Other findings of model estimation indicated that the variables of capital, labor, and fishing distance have a positive and significant effect, while the variables of age, experience, and education level of fishermen have no significant effect on small-scale fisheries production. The main factor that is an obstacle for local fishermen is technology, therefore technology assistance and support from the government are needed as a policy to improve small-scale capture fisheries business and fishermen welfare

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