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
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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Holevo [7,8] introduced such channels and showed that they suffice to demonstrate the”
From An analysis of completely-positive trace-preserving maps on M2 (2002) · cites this paper as [7]
Citations
Cites
Mathematical Foundations of Quantum Mechanics
von Neumann, J. (2018) · Princeton University Press eBooks · doi:10.1515/9781400889921 · Cited by 5,072
General Theory of Banach Algebras.
Batho, E. H., & Rickart, C. E. (1961) · American Mathematical Monthly · doi:10.2307/2312028 · Cited by 1,178
Quantum Field Theories with Composite Particles and Asymptotic Conditions
Haag, R. (1958) · Physical Review · doi:10.1103/physrev.112.669 · Cited by 525
Self-citationQuantum Field Theory in Terms of Vacuum Expectation Values
Wightman, A. S. (1956) · Physical Review · doi:10.1103/physrev.101.860 · Cited by 473
Postulates for General Quantum Mechanics
Segal, I. E. (1947) · Annals of Mathematics · doi:10.2307/1969387 · Cited by 426
Irreducible representations of operator algebras
Segal, I. E. (1947) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1947-08742-5 · Cited by 381
The dual spaces of 𝐶*-algebras
Fell, J. M. G. (1960) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1960-0146681-0 · Cited by 233
Distributions in Hilbert Space and Canonical Systems of Operators
Segal, I. E. (1958) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1958-0102759-x · Cited by 213
Postulates of Quantum Field Theory
Haag, R., & Schroer, B. (1962) · Journal of Mathematical Physics · doi:10.1063/1.1703797 · Cited by 199
Self-citationLes difficultés de divergences pour un modèle particulier de champ quantifié
Hove, L. V. (1952) · Physica · doi:10.1016/s0031-8914(52)80017-5 · Cited by 198
Research works printed but not linked: 9
- 1962, Helv. Phys. Acta, 35, 147
- 1938, Comp. Math., 6, 1
- 1955, Kgl. Danske Videnskab. Selskab Mat.-Fiz. Medd., 29
- 1962, Illinois J. Math., 6, 500
- 1960, Trans. Am. Math. Soc., 94, 365
- 1963, Ann. Physik, 11, 29
- 1943, Mat. Sb., 12, 197
- 1948, Isvertija Ser. Mat., 12, 445
- 1954, Tôhoku Mat. J., 6, 212
Cited by
Sorted by citations
Items 701–800 of 1,000
Locality and entanglement harvesting in covariantly bandlimited scalar fields
Funai, N., & Menicucci, N. C. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.105001 · Cited by 4
Long-distance N-partite information for fermionic CFTs
Agón, C. A., Bueno, P., & van der Velde, G. (2024) · Journal of High Energy Physics · doi:10.1007/jhep12(2024)178 · Cited by 4
Superselection Sectors for Posets of von Neumann Algebras
Bhardwaj, A., Brisky, T., Chuah, C. Y., Kawagoe, K., Keslin, J., Penneys, D., & Wallick, D. (2025) · Communications in Mathematical Physics · doi:10.1007/s00220-025-05315-4 · Cited by 4
Quantum Theory of Irreversibility: Open Systems and Continuum Mechanics
Sewell, G. L. (2003) · Lecture notes in physics · doi:10.1007/3-540-44874-8_1 · Cited by 4
Imperfect Cloning Operations in Algebraic Quantum Theory
Kitajima, Y. (2014) · Foundations of Physics · doi:10.1007/s10701-014-9843-8 · Cited by 4
W∗ -dynamical systems satisfying a spectrum condition
Kraus, J. (1979) · Duke Mathematical Journal · doi:10.1215/s0012-7094-79-04637-4 · Cited by 4
Park, C., Gordji, M. ., & Cho, Y. J. (2012) · Fixed Point Theory and Applications · doi:10.1186/1687-1812-2012-97 · Cited by 4
Quantum correlations with a gap between the sequential and spatial cases
Xu, Z., & Cabello, A. (2017) · Physical Review A · doi:10.1103/physreva.96.012122 · Cited by 4
Entanglement properties of boundary state and thermalization
Guo, W.-Z. (2018) · Journal of High Energy Physics · doi:10.1007/jhep06(2018)044 · Cited by 4
Non‐perturbative Quantum Field Theory and the Geometry of Functional Spaces
Johannes Aastrup, A., & Grimstrup, J. M. (2021) · Fortschritte der Physik · doi:10.1002/prop.202100106 · Cited by 4
Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes
Lewandowski, M. (2022) · Journal of Mathematical Physics · doi:10.1063/5.0055753 · Cited by 4
Quantum Teleportation in the Commuting Operator Framework
Conlon, A., Crann, J., Kribs, D. W., & Levene, R. H. (2022) · Annales Henri Poincaré · doi:10.1007/s00023-022-01255-0 · Cited by 4
Mathematical Reflections on Locality
Guo, L., Paycha, S., & Zhang, B. (2023) · Jahresbericht der Deutschen Mathematiker-Vereinigung · doi:10.1365/s13291-023-00268-w · Cited by 4
Infinite Systems of Classical Particles
Katz, A. (1967) · Journal of Mathematical Physics · doi:10.1063/1.1705179 · Cited by 4
Green operators in low regularity spacetimes and quantum field theory
Hörmann, G., Sanchez, Y. S., Spreitzer, C., & Vickers, J. A. (2020) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab839a · Cited by 4
Some frontiers in constructive quantum field theory and equilibrium statistical mechanics
Fröhlich, J. M. (2008) · Springer eBooks · doi:10.1007/3-540-08853-9_4 · Cited by 4
On the unitarily inequivalent representations in the quantum field theory and the many body problem
Łopuszański, J. T. (1965) · Acta Physica Academiae Scientiarum Hungaricae · doi:10.1007/bf03156463 · Cited by 4
Algebras of observables in the S-matrix approach
Il'in, V. A., & Slavnov, D. A. (1978) · Theoretical and Mathematical Physics · doi:10.1007/bf01035870 · Cited by 4
Independence of group algebras
Conti, R., & Hamhalter, J. (2010) · Mathematische Nachrichten · doi:10.1002/mana.200710038 · Cited by 4
The Relation between KMS States for Different Temperatures
Jäkel, C. D. (2004) · Annales Henri Poincaré · doi:10.1007/s00023-004-0178-4 · Cited by 4
A geometrical model showing the independence of locality and positivity of the energy
Doplicher, S., Regge, T., & Singer, I. M. (1968) · Communications in Mathematical Physics · doi:10.1007/bf01651217 · Cited by 4
Antonsen, F. (1994) · International Journal of Theoretical Physics · doi:10.1007/bf00675166 · Cited by 4
Spectral measures for G2, II: Finite subgroups
Evans, D., & Pugh, M. (2020) · Reviews in Mathematical Physics · doi:10.1142/s0129055x20500269 · Cited by 4
Sheaves and D-Modules on Lorentzian Manifolds
Jubin, B., & Schapira, P. (2016) · Letters in Mathematical Physics · doi:10.1007/s11005-016-0832-z · Cited by 4
Patrascu, A.-T. (2016) · Springer theses · doi:10.1007/978-3-319-46143-4_2 · Cited by 4
Crowther, K. (2016) · Springer eBooks · doi:10.1007/978-3-319-39508-1_3 · Cited by 4
“Above the Slough of Despond”: Weylean invariantism and quantum physics
Toader, I. D. (2017) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2017.04.004 · Cited by 4
Towards a Measurement Theory for Off-Shell Quantum Fields
Okamura, K. (2021) · Symmetry · doi:10.3390/sym13071183 · Cited by 4
Observables, Superselection Sectors and Gauge Groups
Fredenhagen, C. (1992) · NATO ASI series. Series B : Physics · doi:10.1007/978-1-4615-3472-3_6 · Cited by 4
C*- and W*-Algebras of Observables, Their Interpretations, and the Problem of Measurement
Amann, A., & Harald Atmanspacher, A. (1999) · Springer eBooks · doi:10.1007/978-94-011-4581-7_4 · Cited by 4
An Introduction to some Mathematical Aspects of Scattering Theory in Models of Quantum Fields
Albeverio, S. A. (1974) · Springer eBooks · doi:10.1007/978-94-010-2147-0_14 · Cited by 4
Introduction to Quantum Mechanics and the Quantum-Classical transitionPreprint
Cariñena, J. F., Clemente-Gallardo, J., & Marmo, G. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0707.3539 · Cited by 4
Quantum Measurement, Information, and Completely Positive Maps
Ozawa, M. (2006) · Kluwer Academic Publishers eBooks · doi:10.1007/0-306-47114-0_15 · Cited by 6
Haag, R. (2005) · Springer eBooks · doi:10.1007/bfb0034508 · Cited by 4
Self-citationOn the notion of reconstruction of quantum theoryPreprint
Grinbaum, A. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0509104 · Cited by 6
Coupling of space-time and electromagnetic gauge transformations
Cattaneo, U., & Janner, A. (1974) · Journal of Mathematical Physics · doi:10.1063/1.1666787 · Cited by 4
A C∗-algebra formulation of gauge transformations of the second kind for the electromagnetic field
Carey, A. L., Gaffney, J., & Hurst, C. A. (1978) · Reports on Mathematical Physics · doi:10.1016/0034-4877(78)90067-8 · Cited by 4
Noncommutative mean ergodic theorem for partialW *-dynamical semigroups
Ekhaguere, G. O. S. (1993) · International Journal of Theoretical Physics · doi:10.1007/bf00671798 · Cited by 4
Quantum logic and operational quantum mechanics
Abbati, M. C., & Manià, A. (1984) · Reports on Mathematical Physics · doi:10.1016/0034-4877(84)90009-0 · Cited by 4
On the classical content of many-body quantum mechanics
Melsheimer, O. (1979) · Foundations of Physics · doi:10.1007/bf00715179 · Cited by 4
Quantum logic axioms and the proposition-state structure
Gallone, F., & Antonio Zecca, A. (1973) · International Journal of Theoretical Physics · doi:10.1007/bf00671579 · Cited by 4
Representations of Baer ∗ -Semigroups
Gudder, S., & Michel, J. R. (1981) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1981-0593446-0 · Cited by 4
On the algebras of local observables in the generalized sense in quantum mechanics
Wan, K. K., & McLean, R. G. (1985) · Journal of Mathematical Physics · doi:10.1063/1.526770 · Cited by 4
H-images of vector states and causal properties of local algebras
Sushko, V. N., & Horuzhy, S. S. (1973) · Theoretical and Mathematical Physics · doi:10.1007/bf01028219 · Cited by 4
Solutions of classical field equations with locally finite kinetic energy
Parenti, C., Strocchi, F., & Velo, G. (1975) · Physics Letters B · doi:10.1016/0370-2693(75)90691-7 · Cited by 4
Product states and C∗-dynamical system of product type
Baker, B. M., & Powers, R. T. (1983) · Journal of Functional Analysis · doi:10.1016/0022-1236(83)90069-1 · Cited by 4
Some Statistical Problems for Quantum Fields
Холево, А. С. (1973) · Theory of Probability and Its Applications · doi:10.1137/1117038 · Cited by 4
Verch, R. (1996) · arXiv (Cornell University) · doi:10.48550/arxiv.funct-an/9611004 · Cited by 4
The Semiclassical Einstein Equation on Cosmological SpacetimesPreprint
Siemssen, D. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1503.01826 · Cited by 9
Dynamical charges and symmetries in the nonlinear classical field theory
Parenti, C., Strocchi, F., & Velo, G. (1977) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02738185 · Cited by 4
Particle Structure of Gauge Theories
Fredenhagen, K. (1986) · NATO ASI series. Series B : Physics · doi:10.1007/978-1-4757-0363-4_6 · Cited by 4
Effectuses in Categorical Quantum FoundationsPreprint
Cho, K. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1910.12198 · Cited by 8
Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimesPreprint
Lewandowski, M. (2019) · arXiv (Cornell University) · doi:10.25932/publishup-43938 · Cited by 4
Geometric Modular Action and Spontaneous Symmetry BreakingPreprint
Detlev Buchholz, A., & Summers, S. J. (2004) · Cited by 4
Local tomography and the role of the complex numbers in quantum mechanicsPreprint
Niestegge, G. (2020) · PhilSci-Archive (University of Pittsburgh) · Cited by 4
Algebraic Quantum Field Theory: Objectives, Methods, and Results
Detlev Buchholz, A., & Fredenhagen, K. (2024) · Encyclopedia of Mathematical Physics · doi:10.1016/b978-0-323-95703-8.00081-1 · Cited by 4
Determinacy of States and Independence of Operator Algebras
Hamhalter, J. (1998) · International Journal of Theoretical Physics · doi:10.1023/a:1026697003005 · Cited by 4
Logarithmic light cone, slow entanglement growth, and quantum memory
Zeng, Y., Hamma, A., Zhang, Y.-R., Liu, Q., Li, R., Fan, H., & Liu, W.-M. (2025) · Physical review. B./Physical review. B · doi:10.1103/9jbn-nxwz · Cited by 3
Entanglement and correlations between local observables in de Sitter spacetime
Ribes-Metidieri, P., Agulló, I., & Bonga, B. (2026) · Physical review. D/Physical review. D. · doi:10.1103/qqjv-rv8t · Cited by 3
Symmetry, symmetry topological field theory and von Neumann algebra
Jia, Q., & Tian, J. (2026) · Journal of High Energy Physics · doi:10.1007/jhep01(2026)105 · Cited by 3
Reverse Physics: From Laws to Physical Assumptions
Carcassi, G., & Aidala, C. (2022) · Foundations of Physics · doi:10.1007/s10701-022-00555-z · Cited by 3
Gleason’s theorem for composite systems
Frembs, M., & Döring, A. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/acfbcb · Cited by 3
The how, why and wherefore of C*-algebras in statistical mechanics
Hugenholtz, N. M. (2007) · Advances in Solid State Physics · doi:10.1007/bfb0107714 · Cited by 3
Bertozzi, E. (2013) · European Journal of Physics · doi:10.1088/0143-0807/34/3/603 · Cited by 3
An unconventional canonical quantization of local scalar fields over quantum space-time
Banai, M. (1987) · Journal of Mathematical Physics · doi:10.1063/1.527788 · Cited by 3
Superposition, Transition Probabilities and Primitive Observables in Infinite Quantum Systems
Detlev Buchholz, A., & Størmer, E. (2015) · Communications in Mathematical Physics · doi:10.1007/s00220-015-2405-x · Cited by 3
The Limits of Physical Equivalence in Algebraic Quantum Field Theory
Lupher, T. (2016) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/axw017 · Cited by 3
Local and Covariant Flow Relations for OPE Coefficients in Lorentzian Spacetimes
Klehfoth, M., & Wald, R. M. (2023) · Communications in Mathematical Physics · doi:10.1007/s00220-023-04758-x · Cited by 3
Perturbative expansions and the foundations of quantum field theory
Fraser, J. D., & Rejzner, K. (2024) · The European Physical Journal H · doi:10.1140/epjh/s13129-024-00075-6 · Cited by 3
Theoretical Chemistry and More: Personal Annotations to Hans Primas and His Work
Müller‐Herold, U. (2016) · Springer eBooks · doi:10.1007/978-3-319-43573-2_3 · Cited by 3
Coloring Operads for Algebraic Field Theory
Bruinsma, S. (2019) · Fortschritte der Physik · doi:10.1002/prop.201910004 · Cited by 3
Twisted Modules and Pseudo-endomorphisms
Li, H. (2012) · Algebra Colloquium · doi:10.1142/s1005386712000156 · Cited by 3
On the Notion of Composite System
Ciaglia, F. M., Ibort, A., & Marmo, G. (2019) · Lecture notes in computer science · doi:10.1007/978-3-030-26980-7_67 · Cited by 3
Lattice Structure of Intermediate Subfactors
Watatani, Y. (1993) · Springer eBooks · doi:10.1007/978-94-017-2823-2_26 · Cited by 3
Steinmann, O. (2006) · Progress in mathematics · doi:10.1007/978-3-7643-7434-1_21 · Cited by 3
Problems of dynamics in generally covariant quantum field theory
Salehi, H. (1997) · International Journal of Theoretical Physics · doi:10.1007/bf02435777 · Cited by 3
Beyond irreducibility and back
Emch, G. G. (1997) · Reports on Mathematical Physics · doi:10.1016/s0034-4877(97)85915-0 · Cited by 3
Entropy of Quantum Measurement
Podsȩdkowska, H. (2015) · Entropy · doi:10.3390/e17031181 · Cited by 3
Observables and quark confinement in the covariant canonical formalism of Yang-Mills theory III
Ojima, I. (1980) · The European Physical Journal C · doi:10.1007/bf01421780 · Cited by 3
Wigner-Araki-Yanase Theorem in General Theory of Quantum Measurement
Łuczak, A. (2016) · Open Systems & Information Dynamics · doi:10.1142/s123016121650013x · Cited by 3
Local tomography and the role of the complex numbers in quantum mechanics
Niestegge, G. (2020) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2020.0063 · Cited by 3
The Conceptual Basis and Use of the Geometric Invariance Principles
Houtappel, R. M. F., van Dam, H., & Wigner, E. P. (1997) · Springer eBooks · doi:10.1007/978-3-662-09203-3_21 · Cited by 3
Is the Hilbert Space Language Too Rich?
Kupczyński, M. (1978) · Springer eBooks · doi:10.1007/978-94-009-9769-1_3 · Cited by 3
The Quantum Logical and the Operational Description for Physical Systems
Abbati, M. C., & Manià, A. (1981) · Springer eBooks · doi:10.1007/978-1-4613-3228-2_9 · Cited by 3
A Family of Examples with Quantum Constraints
Lledó, F. (1997) · Letters in Mathematical Physics · doi:10.1023/a:1007389608707 · Cited by 3
Von Neumann Algebras and Quantum Field Theory
Longo, R. (1995) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-9078-6_123 · Cited by 3
Quantum information processing and quantum logic: toward mutual illuminationPreprint
Barnum, H. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0205129 · Cited by 3
A canonical formalism of instantons and vacuum tunnelling in the (1+1)-dimensional Higgs model
Ezawa, Z. F. (1979) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02775420 · Cited by 3
An Introduction to C * ‐Algebraic Methods in Physics
Emch, G. G. (1972) · Advances in chemical physics · doi:10.1002/9780470143728.ch4 · Cited by 3
The Quantization of Linear Gravitational Perturbations and the Hadamard Condition
Hunt, D. S. (2012) · White Rose eTheses Online (University of Leeds, The University of Sheffield, University of York) · Cited by 2
Charged Quantum Fields Associated with Endomorphisms of CAR and CCR AlgebrasPreprint
Binnenhei, C. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.math/9809035 · Cited by 3
Tensor Fields on Orbits of Quantum States and Applications
Volkert, G. F. (2010) · Electronic Theses of LMU Munich (Ludwig-Maximilians-Universität München) · doi:10.5282/edoc.11813 · Cited by 3
H-äquivariante Morita-Äquivalenz und DeformationsquantisierungPreprint
Jansen, S. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1004.1656 · Cited by 3
General Covariance in Algebraic Quantum Field TheoryPreprint
Brunetti, R., Porrmann, M., & Ruzzi, G. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.math-ph/0512059 · Cited by 3
Dass, T. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0909.4606 · Cited by 3
An Introduction to Some Topics in Constructive Quantum Field Theory
Fröhlich, J. M. (1978) · Springer eBooks · doi:10.1007/978-1-4615-8924-2_1 · Cited by 3
Some Theorems on Atomicity in Axiomatic Quantum Mechanics
Jenč, F. (1972) · Journal of Mathematical Physics · doi:10.1063/1.1665891 · Cited by 3
An algebraic spectrum condition
Kraus, K. (1970) · Communications in Mathematical Physics · doi:10.1007/bf01646619 · Cited by 3
Local observables, nonlocality, and asymptotically separable quantum mechanics
Wan, K. K. (1988) · Foundations of Physics · doi:10.1007/bf01855941 · Cited by 3
A model for an objective description of macroscopic state variables in quantum mechanics
Lanz, L., Melsheimer, O., & Penati, S. (1986) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(86)90036-1 · Cited by 3
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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
