Conveners
Parallel 4
- Alexander Penin (University of Alberta)
Parallel 4
- Alexander Penin (University of Alberta)
Scattering amplitudes in perturbative quantum field theory exhibit a rich structure of zeros, poles, and branch cuts, which are best understood as varieties in complexified momentum space. It is also well known that scattering amplitudes in gauge theories admit compact representations in the spinor-helicity formalism. However, obtaining such compact representations is often a non-trivial task...
In this presentation I will develop and demonstrate a method to obtain epsilon factorized
differential equations for elliptic Feynman integrals. This method works by choosing an
integral basis with the property that the period matrix obtained by integrating the basis
over a complete set of integration cycles is diagonal. This method is a generalization of a
similar method known to work for...
I will discuss Feynman integrals which depend on more than one elliptic curve and methods to compute them.
We present recent computer algebra tools for Feynman integral.
A special focus will be put on hypergeometric functions and generalization of them
We study integration-by-parts-like relations and differential equations for Feynman integrals in the framework of $\mathcal{D}$-module theory. We leverage the fact that Feynman integrals satisfy a set of PDEs called a GKZ hypergeometric system. This fact allows us to uniquely associate a Feynman integral to an element of a $\mathcal{D}$-module, which can be intepreted as a differential...
Using methods from algebraic geometry such as Gr\"obner bases, we derive operator solutions to IBP relations that retain the functional dependence on the propagator powers $a_i$. The reduction to master integrals is achieved by applying the operators to the integrals $I(a_i)$. The solution at hand makes a case-by-case bottom-up solution of the system of IBP equations obsolete. In the talk we...
