9,022 research outputs found
Some Results on the Complexity of Numerical Integration
This is a survey (21 pages, 124 references) written for the MCQMC 2014
conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov
(1959) and end with new results on the curse of dimension and on the complexity
of oscillatory integrals. Some small errors of earlier versions are corrected
QCD Amplitudes: new perspectives on Feynman integral calculus
I analyze the algebraic patterns underlying the structure of scattering
amplitudes in quantum field theory. I focus on the decomposition of amplitudes
in terms of independent functions and the systems of differential equations the
latter obey. In particular, I discuss the key role played by unitarity for the
decomposition in terms of master integrals, by means of generalized cuts and
integrand reduction, as well as for solving the corresponding differential
equations, by means of Magnus exponential series.Comment: Presented at Rencontres de Moriond 201
- …