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Cited by 1,250Advanced Operator Algebra ResearchQuantum and Classical ElectrodynamicsSpectral Theory in Mathematical Physics

The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.

An Algebraic Approach to Quantum Field Theory

Haag, Rudolf, Kastler, Daniel·1964·Journal of Mathematical Physics
DOI 10.1063/1.1704187
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Abstract

It is shown that two quantum theories dealing, respectively, in the Hilbert spaces of state vectors ℌ1 and ℌ2 are physically equivalent whenever we have a faithful representation of the same abstract algebra of observables in both spaces, no matter whether the representations are unitarily equivalent or not. This allows a purely algebraic formulation of the theory. The framework of an algebraic version of quantum field theory is discussed and compared to the customary operator approach. It is pointed out that one reason (and possibly the only one) for the existence of unitarily inequivalent faithful, irreducible representations in quantum field theory is the (physically irrelevant) behavior of the states with respect to observations made infinitely far away. The separation between such ``global'' features and the local ones is studied. An application of this point of view to superselection rules shows that, for example, in electrodynamics the Hilbert space of states with charge zero carries already all the relevant physical information.

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Show all 18 references

Research works printed but not linked: 9

  1. 1962, Helv. Phys. Acta, 35, 147
  2. 1938, Comp. Math., 6, 1
  3. 1955, Kgl. Danske Videnskab. Selskab Mat.-Fiz. Medd., 29
  4. 1962, Illinois J. Math., 6, 500
  5. 1960, Trans. Am. Math. Soc., 94, 365
  6. 1963, Ann. Physik, 11, 29
  7. 1943, Mat. Sb., 12, 197
  8. 1948, Isvertija Ser. Mat., 12, 445
  9. 1954, Tôhoku Mat. J., 6, 212

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Metadata

Authors
Haag, R., & Kastler, D.
Affiliations
University of Illinois Urbana-Champaign (US)
Venue
Journal of Mathematical Physics
Publisher
AIP Publishing
Published
1964-07-01
Volume
5
Issue
7
Pages
848-861
ISSN
  • 0022-2488 (ISSN-L)
  • 1089-7658
DOI
10.1063/1.1704187
OpenAlex
W1994275197
Cited by
1,250
References
18
Citations by year
2026: 41 · 2025: 26 · 2024: 31 · 2023: 28 · 2022: 26 · 2021: 33 · 2020: 28 · 2019: 63 · 2018: 21 · 2017: 28 · 2016: 28 · 2015: 28 · 2014: 22 · 2013: 10 · 2012: 42
FWCI
16.95
Type
journal article
Language
en
Open access
closed
Locations
Journal of Mathematical Physics (publishedVersion)
Funders
  • National Science Foundation
  • Argonne National Laboratory
Topics
  • Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
  • Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
Keywords
algebraic quantum field theory, faithful representation, unitarily inequivalent representations, irreducible representations, global and local features, superselection rules, electrodynamics, operator approach

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