The Pole Part of the 1PI Four-Point Function in Light-Cone Gauge Yang-Mills Theory

The complete UV-divergent contribution to the one-loop 1PI four-point function of Yang-Mills theory in the light-cone gauge is computed in this paper. The formidable UV-divergent contributions arising from each four-point Feynman diagram yield a succinct final result which contains nonlocal terms as expected. These nonlocal contributions are consistent with gauge symmetry, and correspond to a nonlocal renormalization of the wave function. Renormalization of Yang-Mills theory in the light-cone gauge is thus shown explicitly at the one-loop level.Comment: 35 pages, 18 figures. To be published in Nuc. Phys.

The Three-point Function in Split Dimensional Regularization in the Coulomb Gauge

We use a gauge-invariant regularization procedure, called ``split dimensional regularization'', to evaluate the quark self-energy $\Sigma (p)$ and quark-quark-gluon vertex function $\Lambda_\mu (p^\prime,p)$ in the Coulomb gauge, $\vec{\bigtriangledown}\cdot\vec{A}^a = 0$. The technique of split dimensional regularization was designed to regulate Coulomb-gauge Feynman integrals in non-Abelian theories. The technique which is based on two complex regulating parameters, $\omega$ and $\sigma$, is shown to generate a well-defined set of Coulomb-gauge integrals. A major component of this project deals with the evaluation of four-propagator and five-propagator Coulomb integrals, some of which are nonlocal. It is further argued that the standard one-loop BRST identity relating $\Sigma$ and $\Lambda_\mu$, should by rights be replaced by a more general BRST identity which contains two additional contributions from ghost vertex diagrams. Despite the appearance of nonlocal Coulomb integrals, both $\Sigma$ and $\Lambda_\mu$ are local functions which satisfy the appropriate BRST identity. Application of split dimensional regularization to two-loop energy integrals is briefly discussed.Comment: Latex, 17 pages, 4 figures, uses epsf.sty, epsfig.sty; to appear in Nuc. Phys.

Two-Loop Quark Self-Energy in a New Formalism (II): Renormalization of the Quark Propagator in the Light-Cone Gauge

The complete two-loop correction to the quark propagator, consisting of the spider, rainbow, gluon bubble and quark bubble diagrams, is evaluated in the noncovariant light-cone gauge (lcg). (The overlapping self-energy diagram had already been computed.) The chief technical tools include the powerful matrix integration technique, the n^*-prescription for the spurious poles of 1/qn, and the detailed analysis of the boundary singularities in five- and six-dimensional parameter space. It is shown that the total divergent contribution to the two-loop correction Sigma_2 contains both covariant and noncovariant components, and is a local function of the external momentum p, even off the mass-shell, as all nonlocal divergent terms cancel exactly. Consequently, both the quark mass and field renormalizations are local. The structure of Sigma_2 implies a quark mass counterterm of the form $\delta m (lcg) = m\tilde\alpha_s C_F(3+\tilde\alpha_sW) + {\rm O} (\tilde\alpha_s^3)$, \tilde\alpha_s = g^2\Gamma(\eps)(4\pi)^{\eps -2}, with W depending only on the dimensional regulator epsilon, and on the numbers of colors and flavors. It turns out that \delta m(lcg) is identical to the mass counterterm in the general linear covariant gauge. Our results are in agreement with the Bassetto-Dalbosco-Soldati renormalization scheme.Comment: 36 pages Latex, 5 eps figures, to appear in Nucl.Phys.

QCD Pressure at Two Loops in the Temporal Gauge

We apply the method of \underline{zeta} functions, together with the $n_\mu^*$-prescription for the temporal gauge, to evaluate the thermodynamic pressure in QCD at finite temperature $T$. Working in the imaginary-time formalism and employing a special version of the unified-gauge prescription, we show that the pure-gauge contribution to the pressure at two loops is given by P_2^{\mbox{{\scriptsize gauge}}} = -(g^2/144)N_cN_gT^4, where $N_c$ and $N_g$ denote the number of colours and gluons, respectively. This result agrees with the value in the Feynman gauge.Comment: 19 pages, 2 figures, list of 63 integral

Split dimensional regularization for the Coulomb gauge at two loops

We evaluate the coefficients of the leading poles of the complete two-loop quark self-energy \Sigma(p) in the Coulomb gauge. Working in the framework of split dimensional regularization, with complex regulating parameters \sigma and n/2-\sigma for the energy and space components of the loop momentum, respectively, we find that split dimensional regularization leads to well-defined two-loop integrals, and that the overall coefficient of the leading pole term for \Sigma(p) is strictly local. Extensive tables showing the pole parts of one- and two-loop Coulomb integrals are given. We also comment on some general implications of split dimensional regularization, discussing in particular the limit \sigma \to 1/2 and the subleading terms in the epsilon-expansion of noncovariant integrals.Comment: 32 pages Latex; figures replaced, text unchange

Harmonizing Europe’s payment systems: an uphill battle?

A model is introduced to analyze the effect of network effects and transactions patterns on the decision by banks (not) to standardize payment systems both domestically and across borders. If only a small share of all transactions is cross-border, banks have strong incentives to maintain incompatible standards across countries. The model is applied to the case of harmonizing Europe’s payment networks.economics of technology ;

The Wilson Loop in Yang-Mills Theory in the General Axial Gauge

We test the unified-gauge formalism by computing a Wilson loop in Yang-Mills theory to one-loop order. The unified-gauge formalism is characterized by the abritrary, but fixed, four-vector $N_\mu$, which collectively represents the light-cone gauge $(N^2 = 0)$, the temporal gauge $(N^2 > 0)$, the pure axial gauge $(N^2 < 0)$ and the planar gauge $(N^2 < 0)$. A novel feature of the calculation is the use of distinct sets of vectors, $\{ n_{\mu}, n_{\mu}^{\ast} \}$ and $\{N_{\mu}, N_{\mu}^{\ast}\}$, for the path and for the gauge-fixing constraint, respectively. The answer for the Wilson loop is independent of $N_{\mu}$, and agrees numerically with the result obtained in the Feymman gauge.Comment: 12 pages, 2 figure

More than Words: Communication in Intergroup Conflicts

Numerous studies suggest that communication may be a universal means to mitigate collective action problems. In this study, we challenge this view and show that the communication structure crucially determines whether communication mitigates or intensifies the problem of collective action. We observe the effect of different communication structures on collective action in the context of finitely repeated intergroup conflict and demonstrate that conflict expenditures are significantly higher if communication is restricted to one's own group as compared to a situation with no communication. However, expenditures are significantly lower if open communication within one's own group and between rivaling groups is allowed. We show that under open communication intergroup conflicts are avoided by groups taking turns in winning the contest. Our results do not only qualify the role of communication for collective action but may also provide insights on how to mitigate the destructive nature of intergroup conflicts.Communication, Conflict, Experiment, Rent-seeking

Parental Loss and Schooling: Evidence from Metropolitan Cape Town

This paper makes use of the Cape Area Panel study (CAPS), a longitudinal study of youth and their families in metropolitan Cape Town in order to broaden the empirical body of evidence of the causal impact of parental death on children’s schooling in South Africa in two dimensions. First, analysis of CAPS allows us to examine the extent to which results may generalize across geographically and socioeconomically distinct areas. Second, CAPS allows for an explicit exploration of whether the causal impact lessens as time since the parental death lengthens. Evidence from the CAPS is consistent with that from a large demographic surveillance site in rural KwaZulu-Natal in supporting the findings that mother’s deaths have a causal impact on children’s schooling outcomes and that there is no evidence of a causal effect of paternal loss on schooling for African children. The loss of a father has a significant negative impact on the education of coloured children but a significant amount of this impact is driven by socioeconomic status. We exploit the longitudinal data to investigate the extent to which orphan disadvantage precedes parental death and whether orphans begin to recover in the period following a parent’s death or whether they continue to fall behind. We find no evidence of orphan recovery in the period following their parent’s death and results suggest that negative impacts increase with the time since the parent died. The longer-run impact of parental death in childhood is also evident in an analysis of the completion of secondary schooling by early adulthood. These results suggest that parental death will reduce the ultimate human capital attainment of the child.