Probing the Consistency of Quantum Field Theory I: From Nonconvergence to Haag's Theorem (1949–1954)

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Alexander S. Blum (Munich Center for Mathematical Philosophy and Max Planck Institute for the History of Science)

Probing the Consistency of Quantum Field Theory I

Name: Probing the Consistency of Quantum Field Theory I
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ISBN: 9781009265331

From Nonconvergence to Haag's Theorem (1949–1954)

Alexander S. Blum (Munich Center for Mathematical Philosophy and Max Planck Institute for the History of Science)

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English

Cambridge University Press
26 February 2026

Philosophy of science; History of science; Quantum physics (quantum mechanics & quantum field theory); Relativity physics

Series: Elements in the Foundations of Contemporary Physics

Summary
Details

This two‐volume 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.

By: Alexander S. Blum (Munich Center for Mathematical Philosophy and Max Planck Institute for the History of Science)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Weight: 181g
ISBN: 9781009265331
ISBN 10: 1009265334
Series: Elements in the Foundations of Contemporary Physics
Pages: 116
Publication Date: 26 February 2026
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active