Novel aspects of scattering equations

The scattering equations, a system of algebraic equations connecting the space of kinematic invariants and the moduli space of punctured Riemann spheres, provide a new way to construct scattering amplitudes. In this novel framework, the tree-level S-matrix in many quantum field theories can be reformulated as a multiple integral that is entirely localized on the zeroes of the scattering equations. The aim of this thesis is to deepen our understanding of the physical and mathematical structures underlying the scattering equations and to broaden the scope for their applications. In particular, we analyze and extend the scattering equations to on-shell amplitudes in several effective field theories and form factors that carry off-shell momenta in gauge theory. We also study the asymptotic behavior of the scattering equations in various Regge kinematic regimes and derive the corresponding factorizations of amplitudes in gauge theory and gravity. Finally, we propose the physical homotopy continuation of the scattering equations and develop an efficient method to solve these equations.(SC - Sciences) -- UCL, 201