Probing the consistency of quantum field theory I : from nonconvergence to Haag's theorem (1949-1954) / Alexander S. Blum.

Format:

Book

Author/Creator:

Blum, Alexander S. (Alexander Simon), author.

Series:

Cambridge elements. Elements in the foundations of contemporary physics

Cambridge elements. Elements in the foundations of contemporary physics, 2752-3039

Language:

English

Subjects (All):

Quantum field theory.

Physical Description:

1 online resource.

Place of Publication:

Cambridge : Cambridge University Press, 2026.

Summary:

"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"-- Cambridge Core.

Contents:

The divergence of the perturbation series

The search for nonperturbative solutions

Infinite renormalization and UV behavior

The axiomatic approach

Notes:

Includes bibliographical references

Online resource; title from PDF title page (Cambridge Core, viewed February 6, 2026).

Other Format:

Print version: Blum, Alexander S. (Alexander Simon) Probing the consistency of quantum field theory I

ISBN:

9781009265362

1009265369

OCLC:

1552150976

Publisher Number:

CIPO000304526

Access Restriction:

Some versions: Open access versions available from some providers open access