Probing the Consistency of Quantum Field Theory I

This twövolume Element reconstructs and analyzes the historical debates on whether renormalized quantum field theory is a mathematically consistent theory. This volume covers the years the years immediately following the development of renormalized quantum electrodynamics. It begins with the realization that perturbation theory cannot serve as the foundation for a proof of consistency, due to the non-convergence of the perturbation series. Various attempts at a nonperturbative formulation of quantum field theory are discussed, including the Schwinger-Dyson equations, GunnarKällén's nonperturbative renormalization, the renormalization group of MurrayGell-Mann and Francis Low, and, in the last section, early axiomatic quantum field theory. The second volume of this Element covers the establishment of Haag's theorem, which proved that even the Hilbert space of perturbation theory is an inadequate foundation for a consistent theory. This title is also available as Open Access on Cambridge Core.

List of contents

1. Introduction; 2. The divergence of the perturbation series; 3. The search for non-perturbative solutions; 4. Infinite renormalization and UV behavior; 5. The axiomatic approach; Archives consulted; References.

Product details

• Authors: Alexander S. Blum, Alexander S. (Munich Center for Mathematical Blum
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Release: 31.12.2025
• EAN: 9781009265331
• ISBN: 978-1-0-0926533-1
• Series: Elements in the Foundations of Contemporary Physics
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > General, dictionaries; SCIENCE / Physics / General, Philosophy of Science, History of Science, Quantum physics (quantum mechanics & quantum field theory), Quantum physics (quantum mechanics and quantum field theory), Relativity physics