Numerical evaluation of complex amplitudes coefficients using finite fields

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