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Cited by 269Advanced Operator Algebra ResearchAlgebraic structures and combinatorial modelsBlack Holes and Theoretical Physics

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Modular structure of the local algebras associated with the free massless scalar field theory

Hislop, Peter D., Longo, Roberto·1982·Communications in Mathematical Physics
DOI 10.1007/bf01208372
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Research works printed but not linked: 21

  1. Bisognano, J. J., Wichmann, E. H.: On the duality condition for a Hermitian scalar field. J. Math. Phys.16, 985?1007 (1975) · DOI
  2. Buchholz, D.: On the structure of local quantum fields with non-trivial interaction. In: Proc. of the Int. Conf. on Operator Algebras, Ideals and their Application in Theoretical Physics, Baumgärtel, Lassner, Pietsch, Uhlmann, (eds.) pp. 146?153. Leipzig: Teubner Verlagsgesell schaft 1978
  3. Bisognano, J. J., Wichmann, E. H.: On the duality condition for quantum fields. J. Math. Phys.17, 303?321 (1976) · DOI · Paper page
  4. Swieca, J. A., Völkel, A. H.: Remarks on conformal invariance. Commun. Math. Phys.24, 319?342 (1973) · DOI
  5. Courant, R., Hilbert, D.: Methods of mathematical physics, Vol. II. New York: Interscience Publishers, pp. 668?691 1962
  6. Driessler, W.: On the type of local algebras in quantum field theory. Commun. Math. Phys.53, 295?297 (1977) · DOI
  7. Longo, R.: Notes on algebraic invariants for non-commutative dynamical systems. Commun. Math. Phys.69, 195?207 (1979) · DOI
  8. Araki, H.: A lattice of von Neumann algebras associated with the quantum theory of a free bose field. J. Math. Phys.4, 1343?1362 (1963) · DOI
  9. Benfatto, G., Nicolò, F.: The local von Neumann algebras for the massless scalar free field and the free electromagnetic field. J. Math. Phys.19, 653?660 (1978) · DOI
  10. Araki, H., Woods, E. J.: A classification of factors. Publ. R.I.M.S., Kyoto Univ.4A, 51?130 (1968) · DOI
  11. Eckmann, J. P., Fröhlich, J.: Unitary equivalence of local algebras in the quasifree representation. Ann. Inst. Henri Poincaré20A, 201?209 (1974)
  12. Glimm, J., Jaffe, A.: The ?(?4)2 quantum field theory without cutoffs: III. The physical vacuum. Acta Math. (Uppsala)125, 203?261 (1970) · DOI
  13. Araki, H.: Von Neumann algebras of local observables for free scalar field. J. Math. Phys.5, 1?13 (1964) · DOI
  14. Vladimirov, V. S.: Les fonctions de plusieurs variables complexes et leur application à la théorie quantique des champs, Lagowski, N. (tr.) Paris: Dunod 1967
  15. Hortaçsu, M., Seiler, R., Schroer, B.: Conformal symmetry and reverberations. Phys. Rev.5D, 2519?2534 (1972)
  16. Gross, L.: Norm invariance of mass-zero equations under the conformal group. J. Math. Phys.5, 687?695 (1964) · DOI
  17. Borchers, H. J.: Field operators asC ? functions in spacelike directions. Nuovo Cimento33, 1600?1613 (1964) · DOI
  18. Doplicher, S., Haag, R., Roberts, J. E.: Fields, observables and gauge transformations I. Commun. Math. Phys.13, 1?23 (1969) · DOI
  19. Rieffel, M. A.: A commutation theorem and duality for free bose fields. Commun. Math. Phys.39, 153?164 (1974) · DOI
  20. Araki, H.: ?A generalization of Borchers theorem. Helv. Phys. Acta36, 132?139 (1963)
  21. Leyland, P., Roberts, J. E., Testard, D.: Duality for quantum free fields. Marseille Preprint 1978

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Metadata

Authors
Hislop, P. D., & Longo, R.
Affiliations
  • University of California, Berkeley (US)
  • Sapienza University of Rome (IT)
ORCID
Venue
Communications in Mathematical Physics
Publisher
Springer Science and Business Media LLC
Published
1982-03
Volume
84
Issue
1
Pages
71-85
ISSN
  • 0010-3616 (ISSN-L)
  • 1432-0916
DOI
10.1007/bf01208372
OpenAlex
W1976421249
Cited by
269
References
0
Citations by year
2026: 8 · 2025: 14 · 2024: 18 · 2023: 21 · 2022: 22 · 2021: 15 · 2020: 19 · 2019: 20 · 2018: 14 · 2017: 12 · 2016: 8 · 2015: 2 · 2014: 7 · 2013: 7 · 2012: 1
FWCI
2.84
Type
journal article
Language
en
Open access
closed
Licence
www.springer.com/tdm (tdm)
Locations
  • Communications in Mathematical Physics (publishedVersion)
  • Project Euclid (Cornell University) (submittedVersion)
Topics
  • Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
  • Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
Keywords
modular structure, local algebras, modular automorphism group, modular conjugation, conformal group, Möbius transformations, type III_1 factors, unitary equivalence, Minkowski space

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CoChat. (2026). Citation check: Modular structure of the local algebras associated with the free massless scalar field theory. https://app.cochat.ai/papers/10.1007/bf01208372
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Hislop, P. D., & Longo, R. (1982). Modular structure of the local algebras associated with the free massless scalar field theory. Communications in Mathematical Physics. https://doi.org/10.1007/bf01208372