Perturbative quantum electrodynamics and axiomatic field theory

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This book explores relativistic quantum field theory, focusing on QED, its most successful instance. It occupies a unique space between the mathematically rigorous yet numerically limited general field theory favored by mathematical physicists and the more computationally rich but occasionally mathematically adventurous field theory of phenomenologists. The goal is to foster closer ties between these two distinct cultures for mutual benefit. Perturbative QED serves as a key example, illustrating how the rules of perturbative quantum field theory—crucial for phenomenology—can be derived from well-defined general assumptions in a mathematically rigorous manner, without relying on regularizations. The text emphasizes the importance of addressing the infrared problem comprehensively. This approach leads to an unconventional method based on the local-observables framework to describe particles and their interactions. The resulting scattering formalism is directly applicable to the infraparticle scenario in QED, providing observable-inclusive cross-section expressions that do not depend on the S matrix concept. Notably, these expressions differ from those derived through conventional methods, potentially sparking engaging discussions. The author has been exploring these issues for an extended period.