$$\hbox {Next-to}{}^k$$ Leading Log Expansions by Chord Diagrams

@article{Courtiel2020hboxL,
  title={\$\$\hbox \{Next-to\}\{\}^k\$\$ Leading Log Expansions by Chord Diagrams},
  author={Julien Courtiel and Karen A. Yeats},
  journal={Communications in Mathematical Physics},
  year={2020}
}
Green functions in a quantum field theory can be expanded as bivariate series in the coupling and a scale parameter. The leading logs are given by the main diagonal of this expansion, i.e. the subseries where the coupling and the scale parameter appear to the same power; then the next-to leading logs are listed by the next diagonal of the expansion, where the power of the coupling is incremented by one, and so on. We give a general method for deriving explicit formulas and asymptotic estimates… 
Log expansions from combinatorial Dyson–Schwinger equations
  • O. Kruger
  • Mathematics
    Letters in Mathematical Physics
  • 2020
We give a precise connection between combinatorial Dyson–Schwinger equations and log expansions for Green’s functions in quantum field theory. The latter are triangular power series in the coupling
Log expansions from combinatorial Dyson–Schwinger equations
We give a precise connection between combinatorial Dyson–Schwinger equations and log expansions for Green’s functions in quantum field theory. The latter are triangular power series in the coupling
Dyson-Schwinger Equations in Minimal Subtraction
We examine selected one-scale Dyson-Schwinger-equations in the minimal subtraction renormalization scheme and dimensional regularization. They are constructed from three different integral kernels;
Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: phi3 QFT in 6 Dimensions
We analyze the asymptotically free massless scalar φ quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative
Tropical Monte Carlo quadrature for Feynman integrals
We introduce a new method to evaluate algebraic integrals over the simplex numerically. It improves upon geometric sector decomposition by employing tools from tropical geometry. The method can be
Connected Chord Diagrams and Bridgeless Maps
TLDR
A bijection is described between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorsial maps on the other hand, which naturally extends to indecomposable diagrams and general rooted maps.
University of Birmingham Connected chord diagrams and bridgeless maps
We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on the other hand. We
The combinatorics of a tree-like functional equation for connected chord diagrams
We build on recent work of Yeats, Courtiel, and others involving connected chord diagrams. We first derive from a Hopf-algebraic foundation a class of tree-like functional equations and prove that

References

SHOWING 1-10 OF 22 REFERENCES
Log expansions from combinatorial Dyson–Schwinger equations
We give a precise connection between combinatorial Dyson–Schwinger equations and log expansions for Green’s functions in quantum field theory. The latter are triangular power series in the coupling
Growth estimates for Dyson-Schwinger equations
Dyson-Schwinger equations are integral equations in quantum field theory that describe the Green functions of a theory and mirror the recursive decomposition of Feynman diagrams into subdiagrams.
Angles, Scales and Parametric Renormalization
We discuss the structure of renormalized Feynman rules. Regarding them as maps from the Hopf algebra of Feynman graphs to $${\mathbb{C}}$$ originating from the evaluation of graphs by Feynman rules,
Perturbation expansions at large order: results for scalar field theories revisited
  • A. McKane
  • Physics
    Journal of Physics A: Mathematical and Theoretical
  • 2019
The question of the asymptotic form of the perturbation expansion in scalar field theories is reconsidered. Renewed interest in the computation of terms in the -expansion, used to calculate critical
The QCD β-function from global solutions to Dyson–Schwinger equations
Terminal chords in connected chord diagrams
Rooted connected chord diagrams form a nice class of combinatorial objects. Recently they were shown to index solutions to certain Dyson-Schwinger equations in quantum field theory. Key to this
Quantum periods: A census of \phi^4-transcendentals
Perturbative quantum field theories frequently feature rational linear combinations of multiple zeta values (periods). In massless \phi^4-theory we show that the periods originate from certain
...
...