82 citations · 437 across the 28 of their papers we have counts for
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math-ph2020★ 57 cited
Tropical Monte Carlo quadrature for Feynman integrals
Michael Borinsky
We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of…
hep-th2020★ 39 cited
Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations
Michael Borinsky, Gerald V. Dunne
For certain quantum field theories, the Kreimer-Connes Hopf-algebraic approach to renormalization reduces the Dyson-Schwinger equations to a system of non-linear ordinary different…
hep-th2020★ 18 cited
The Hopf algebra structure of the -operation
Robert Beekveldt, Michael Borinsky, Franz Herzog
We give a Hopf-algebraic formulation of the -operation, which is a canonical way to render UV and IR divergent Euclidean Feynman diagrams finite. Our analysis uncovers a close…