Karen Yeats

An Étude in non-linear Dyson–Schwinger Equations ⁎

We show how to use the Hopf algebra structure of quantum field theory to derive nonperturbative results for the short-distance singular sector of a renormalizable quantum field theory in a simple but generic example. We discuss renormalized Green functions G R ( α , L ) in such circumstances which depend on a single scale L = ln q 2 / μ 2 and start from an expansion in the scale G R ( α , L ) = 1 + ∑ k γ k ( α ) L k . We derive recursion relations between the γ k which make full use of the renormalization group. We then show how to determine the Green function by the use of a Mellin transform on suitable integral kernels. We exhibit our approach in an example for which we find a functional equation relating weak and strong coupling expansions.

Spanning Forest Polynomials and the Transcendental Weight of Feynman Graphs

We give combinatorial criteria for predicting the transcendental weight of Feynman integrals of certain graphs in

Recursion and Growth Estimates in Renormalizable Quantum Field Theory

{\phi^4}

Forbidden minors for graphs with no first obstruction to parametric Feynman integration

theory. By studying spanning forest polynomials, we obtain operations on graphs which are weight-preserving, and a list of subgraphs which induce a drop in the transcendental weight.

A four-vertex, quadratic, spanning forest polynomial identity

Abstract We study quantum chromodynamics from the viewpoint of untruncated Dyson–Schwinger equations turned to an ordinary differential equation for the gluon anomalous dimension. This non-linear equation is parameterized by a function P(x) which is unknown beyond perturbation theory. Still, very mild assumptions on P(x) lead to stringent restrictions for possible solutions to Dyson–Schwinger equations. We establish that the theory must have asymptotic freedom beyond perturbation theory and also investigate the low energy regime and the possibility for a mass gap in the asymptotically free theory.

A combinatorial understanding of lattice path asymptotics

In this paper we show that there is a Lipatov bound for the radius of convergence for superficially divergent one-particle irreducible Green functions in a renormalizable quantum field theory if there is such a bound for the superficially convergent ones. In the nonnegative case the radius of convergence turns out to be min{ρ,1/b1}, where ρ is the bound on the convergent ones, the instanton radius, and b1 the first coefficient of the β-function, while in general it is bounded by the above.

The size of characters of exceptional lie groups

A bstractWe study the splitting functions for the evolution of fragmentation distributions and the coefficient functions for single-hadron production in semi-inclusive e+e− annihilation in massless perturbative QCD for small values of the momentum fraction and scaling variable x, where their fixed-order approximations are completely destabilized by huge double logarithms of the form

On the set of zero coefficients of a function satisfying a linear differential equation

\alpha_{\mathrm{s}}^n{x^{-1 }}\mathrm{l}{{\mathrm{n}}^{2n - a }}x