This is the page for the seminar series on motives and period integrals in Quantum field theory and String theory.
The seminars are taking place in an hybrid form. The Zoom Meeting ID and the password, will be sent to the participants by email before the semaine via the mailing list
If you are interested in joining this seminar series you should contact the organisers.
We provide evidence through two loops, that rational letters of polylogarithmic Feynman integrals are captured by the Landau equations, when the latter are recast as a polynomial of the kinematic variables of the integral, known as the principal A-determinant. Focusing on one loop, we further show how to also obtain all non-rational letters with the help of Jacobi determinant identities. We verify our findings by explicitly constructing canonical differential equations and comparing with the existing literature, and finally extend the proof of the Cohen-Macauley property of one-loop integrals to a broader range of their kinematics.
Nowadays, perturbative calculations in quantum field theory provide a lucky combination of practical importance and mathematical depth. In this talk I will review some modern methods of multiloop calculations: parametric representations, IBP reduction, differential equations and dimensional recurrences. I will also discuss some open questions and new approaches which may be important for further development of multiloop methods.
I present various symbolic methods that are applied in
an ongoing long term cooperation between RISC and DESY (Deutsches
Elektronen-Synchrotron) to tackle massive 3-loop Feynman integrals.
Special emphasis is put on computer algebra tools from symbolic summation
and integration and the large moment method which is the basis
to guess linear difference and differential equations for the underlying physical problem.
Feynman integrals are essential ingredients for the computation of higher order corrections to observables in collider experiments. Their analytic properties led long time ago to the conjecture that they belong to a generalized class of hypergeometric functions. In this talk, I will discuss the relation between Feynman integrals in parametric representation and A-hypergeometric functions, introduced in the late '80s by Gel'fand, Kapranov, and Zelevinsky (GKZ). I will give a brief review of A-hypergeometric functions and the differential equations they satisfy in order to show how Feynman integrals can be naturally understood as A-hypergeometric functions. I will then show how this knowledge provides a practical method to evaluate Feynman integrals using computational algebraic geometry and give some examples. Finally, inspired by GKZ, I will mention how differential equations can be set for full scattering amplitudes.
17 January 2024
Time: 11h00 (Paris, France Time)
Simon Telen
Max Planck institute for Mathematics in the Sciences in Leipzig
Hybrid talk from room VC1 in the TCC room at the Mathematical Institute of the University of Oxford and on zoom
pdf de l'exposé
Computational algebraic geometry for Landau analysis
I will present algebraic methods for computing singular loci of Feynman integrals as functions of kinematic parameters. I will demonstrate how our implementation of these methods can tackle challenging diagrams which were previously out of reach. Our approach applies to a more general class of integrals, called Euler integrals, which are twisted periods of very affine varieties. This is joint work with Claudia Fevola and Sebastian Mizera.
