New formalism of quantum field theory

Abstract

In recent years, theoretical calculations of scattering amplitudes face a huge challenge because experiment data coming from colliders, such as Large Hadron Collider (LHC), become more and more accurate. The traditional Feynman diagram technique can not deal with the problem because the difficulties involving gauge interaction. To solve the problem, theorists have made many studies. Through investigations of last fourteen years, we have achieved many important progresses, such as on-shell recursion relation, the Cachazo-He-Yuan framework for scattering amplitudes of massless particles, the geometric Grassmannian and Amplituhedron frameworks for N =4 SYM planar amplitudes, etc. These new methods can calculate tree-level and loop scattering amplitudes much faster than the traditional method, so have improved our ability to analyze background contributions from Standard Model and find possible signals of new physics by comparing with experiment data. These breakthroughs have some common features. These features, such as the focus of on-shell properties, the right choice of prescription variables and the emphasize of the analytic properties of scattering amplitudes, hint a possible new formalism of quantum field theory, which is very different from traditional Lagrangian formalism. In this article, we give a brief discussion of this topic.