# Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: phi3 QFT in 6 Dimensions

@article{Borinsky2021SemiclassicalTF, title={Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: phi3 QFT in 6 Dimensions}, author={Michael Borinsky and Gerald V. Dunne and Max Meynig}, journal={Symmetry, Integrability and Geometry: Methods and Applications}, year={2021} }

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 completion of the divergent perturbative solutions to the Kreimer–Connes Hopf-algebraic Dyson–Schwinger equations for the anomalous dimension. This scalar conformal field theory is asymptotically free and has a real Lipatov instanton. In the Hopf-algebraic approach we find a trans-series having an…

## 6 Citations

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