Corpus ID: 221370588

Tropical Monte Carlo quadrature for Feynman integrals

@article{Borinsky2020TropicalMC,
  title={Tropical Monte Carlo quadrature for Feynman integrals},
  author={Michael Borinsky},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
  • Michael Borinsky
  • Published 2020
  • Mathematics, Physics
  • arXiv: Mathematical Physics
  • 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 improved further by exploiting the geometric structure of the underlying integrand. As an illustration of this, we give a specialized algorithm for a class of integrands that exhibit the form of a generalized permutahedron. This class includes integrands for scattering amplitudes and parametric… CONTINUE READING
    1 Citations

    Figures and Tables from this paper.

    Collider Physics at the Precision Frontier
    • 5
    • PDF

    References

    SHOWING 1-10 OF 104 REFERENCES
    Analytic Tools for Feynman Integrals
    • 146
    • PDF
    Lectures on differential equations for Feynman integrals
    • 171
    • PDF
    Toric geometry and regularization of Feynman integrals.
    • 6
    • PDF
    An automatized algorithm to compute infrared divergent multi-loop integrals
    • 367
    • Highly Influential
    • PDF
    Euler-Mellin integrals and A-hypergeometric functions
    • 17
    • PDF
    Multiloop integrals in dimensional regularization made simple.
    • J. Henn
    • Mathematics, Medicine
    • Physical review letters
    • 2013
    • 428
    • PDF
    Resolution of singularities for multi-loop integrals
    • 136
    • PDF
    Renormalized asymptotic enumeration of Feynman diagrams
    • 20
    • PDF
    New differential equations for on-shell loop integrals
    • 47
    • PDF