Aspects of scattering amplitudes in scalar effective field theories
Quantum field theory provides a fundamental framework for describing interactions among elementary particles. Its central observables, scattering amplitudes, encode precise quantitative information about particle scattering processes. In this thesis, Yang Li investigates the scattering amplitudes of a class of scalar field theories, treating them as analytic functions and uncovering a range of nontrivial algebraic structures. These structures are shown to be deeply connected to the underlying physical properties of the particles involved.
Li's analysis reveals that seemingly abstract mathematical features of amplitudes reflect concrete physical principles, offering new insights into the nature of particle interactions. By systematically exploring these connections, this work establishes a bridge between modern amplitude-based approaches and the traditional formulations of quantum field theory. In doing so, it not only clarifies the mathematical organization of scattering processes but also exposes previously hidden aspects of their physical behavior.
Overall, the results highlight the power of analytic and algebraic methods in advancing our understanding of fundamental interactions, suggesting new directions for both theoretical development and the interpretation of physical phenomena.