Numerical evaluation of complex\namplitudes coefficients using finite fields

The calculation of scattering amplitudes is an essential task for high-precision theoretical
\npredictions. It often represents a major bottleneck when processes with a high
\nnumber of loops and legs are considered. In this thesis we present a method for the evaluation
\nof complex coefficients of amplitudes for physical phase-space points with finite fields
\ntechniques. The algorithm is suitable for any rational function of complex invariants,
\nincluding tree-level amplitudes and rational coefficients of complex amplitudes. Since it
\nrelies on finite fields and rational reconstruction, it is free of the numerical instabilities
\nwhich affect floating-point evaluations. We employ and test this method in combination
\nwith the spinor helicity formalism and the momentum twistor parametrization. We
\nimplemented these methods in Mathematica routine with the use of FiniteFlow.