Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions

Stephen J. Summers; Reinhard Werner

Annales de l'I.H.P. Physique théorique (1988)

  • Volume: 49, Issue: 2, page 215-243
  • ISSN: 0246-0211

How to cite

top

Summers, Stephen J., and Werner, Reinhard. "Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions." Annales de l'I.H.P. Physique théorique 49.2 (1988): 215-243. <http://eudml.org/doc/76413>.

@article{Summers1988,
author = {Summers, Stephen J., Werner, Reinhard},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Bell's inequalities; quantum field theory; maximally correlated Von Neumann algebras; complementary wedge algebras; tangent double cone algebras; algebras for tangent space time regions; field theories with a scaling limit},
language = {eng},
number = {2},
pages = {215-243},
publisher = {Gauthier-Villars},
title = {Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions},
url = {http://eudml.org/doc/76413},
volume = {49},
year = {1988},
}

TY - JOUR
AU - Summers, Stephen J.
AU - Werner, Reinhard
TI - Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions
JO - Annales de l'I.H.P. Physique théorique
PY - 1988
PB - Gauthier-Villars
VL - 49
IS - 2
SP - 215
EP - 243
LA - eng
KW - Bell's inequalities; quantum field theory; maximally correlated Von Neumann algebras; complementary wedge algebras; tangent double cone algebras; algebras for tangent space time regions; field theories with a scaling limit
UR - http://eudml.org/doc/76413
ER -

References

top
  1. [1] C. D'Antoni and R. Longo, Interpolation by type I factors and the flip automorphism. J. Funct. Anal., t. 51, 1983, p. 361-371. Zbl0535.46036MR703083
  2. [2] C. D'Antoni, D. Buchholz and K. Fredenhagen, The universal structure of local algebras. Commun. Math. Phys., t. 111, 1987, p. 123-135. Zbl0645.46048MR896763
  3. [3] H. Araki, Local quantum theory, I. In: Local Quantum Theory, ed. R. Jost, Academic Press, New York, 1969. 
  4. [4] H. Araki, Asymptotic ratio set and property L'λ. Publ. RIMS, Kyoto Univ., t. 6, 1970-1071, p. 443-460. Zbl0231.46100MR308800
  5. [5] H. Araki and E.J. Woods, A classification of factors. Publ. RIMS, Kyoto Univ., t. 4, 1968, p. 51-130. Zbl0206.12901MR244773
  6. [6] D. Buchholz, Product states for local algebras. Commun. Math. Phys., t. 36, 1974, p. 287-304. Zbl0289.46050MR345546
  7. [7] D. Buchholz and K. Fredenhagen, Locality and the structure of particle states. Commun. Math. Phys., t. 84, 1982, p. 1-54. Zbl0498.46061MR660538
  8. [8] D. Buchholz and E.H. Wichmann, Causal independence and the energy-level density of states in local quantum field theory. Commun. Math. Phys., t. 106, 1986, p. 321-344. Zbl0626.46064MR855315
  9. [9] D. Buchholz, S. Doplicher and R. Longo, On Noether's theorem in quantum field theory. Ann. Phys., t. 170, 1986, p. 1-17. Zbl0609.46037MR848392
  10. [10] B.S. Cirel'son, Quantum generalizations of Bell's inequalities. Lett. Math. Phys., t. 4, 1980, p. 93-100. MR577178
  11. [11] A. Connes and E. Størmer, Homogeneity of the state space of factors of type III1. J. Funct. Anal., t. 28, 1978, p. 187-196. Zbl0408.46048MR470689
  12. [12] S. Doplicher, R. Haag and J.E. Roberts, Fields, observables and gauge transformations, I, II. Commun. Math. Phys., t. 13, 1969, p. 1-23 and t. 15, 1969, p. 173- 200. Zbl0175.24704MR258394
  13. [13] S. Doplicher and R. Longo, Standard and split inclusions of von Neumann algebras. Invent. Math., t. 75, 1984, p. 493-536. Zbl0539.46043MR735338
  14. [14] W. Driessler, Comments on lightlike translations and applications in relativistic quantum field theory. Commun. Math. Phys., t. 44, 1975, p. 133-141. Zbl0306.46076MR416336
  15. [15] W. Driessler, On the type of local algebras in quantum field theory. Commun. Math. Phys., t. 53, 1977, p. 295-297. Zbl0348.46055MR473853
  16. [16] W. Driessler, On the structure of fields and algebras on null planes, I, Local algebras. Acta Phys. Austr., t. 46, 1977, p. 63-96. MR468834
  17. [17] W. Driessler, Duality and absence of locally generated superselection sectors for CCR-type algebras. Commun. Math. Phys., t. 70, 1979, p. 213-220. Zbl0427.46047MR554492
  18. [18] W. Driessler and S.J. Summers, Central decomposition of Poincaré-invariant nets of local field algebras and absence of spontaneous breaking of the Lorentz group. Ann. Inst. Henri Poincaré, t. A 43, 1985, p. 147-166. Zbl0609.47059MR817532
  19. [19] W. Driessler and S.J. Summers, On the decomposition of relativistic quantum field theories into pure phases. Helv. Phys. Acta, t. 59, 1986, p. 331-348. MR845432
  20. [20] W. Driessler, S.J. Summers and E.H. Wichmann, On the connection between quantum fields and von Neumann algebras of local operators. Commun. Math. Phys., t. 105, 1986, p. 49-84. Zbl0595.46062MR847127
  21. [21] J.-P. Eckmann and J. Fröhlich, Unitary equivalence of local algebras in the quasi-free representation. Ann. Inst. Henri Poincaré, t. A 20, 1974, p. 201-209. Zbl0287.46077MR400966
  22. [22] J.D. Fabrey, Exponential representations of the canonical commutation relations. Commun. Math. Phys., t. 19, 1970, p. 1-30. Zbl0197.26302MR272311
  23. [23] K. Fredenhagen, On the modular structure of local algebras of observables. Commun. Math. Phys., t. 97, 1985, p. 79-89. Zbl0582.46067MR782959
  24. [24] J. Glimm and A. Jaffe, The λ(φ4)2 quantum field theory without cutoffs. III. The physical vacuum. Acta Math., t. 125, 1970, p. 204-267. MR269234
  25. [25] R. Haag and D. Kastler, An algebraic approach to quantum field theory. J. Math. Phys., t. 5, 1964, p. 848-861. Zbl0139.46003MR165864
  26. [26] P.D. Hislop and R. Longo, Modular structure of the local algebras associated with the free massless scalar field theory. Commun. Math. Phys., t. 84, 1982, p. 71-85. Zbl0491.46060MR660540
  27. [27] P.D. Hislop, Conformal covariance, modular structure and duality for local algebras in free massless quantum field theories, preprint, University of California, 1987. MR965577
  28. [28] L.J. Landau, On the violation of Bell's inequality in quantum theory. Phys. Lett., t. 120 A, 1987, p. 54-56. MR879718
  29. [29] O.A. Nielsen, The asymptotic ratio set and direct integral decompositions of a von Neumann algebra. Can. J. Math., t. 23, 1971, p. 598-607. Zbl0217.16902MR298433
  30. [30] R.T. Powers, Representations of uniformly hyperfinite algebras and their associated von Neumann rings. Ann. Math., t. 86, 1967, p. 138-171. Zbl0157.20605MR218905
  31. [31] R.T. Powers, UHF algebras and their applications to representations of the anticommutation relations. In: Cargèse Lectures in Physics, Vol. 4, ed. D. Kastler, Gordon and Breach, New York, London, Paris, 1970. 
  32. [32] J.E. Roberts, Some applications of dilatation invariance to structural questions in the theory of local observables. Commun. Math. Phys., t. 37, 1974, p. 273-286. Zbl0292.46031MR368650
  33. [33] H. Roos, Independence of local algebras in quantum field theory. Commun. Math. Phys., t. 16, 1970, p. 238-246. Zbl0197.26303MR266539
  34. [34] S. Sakai, C*-Algebras and W*-Algebras. Springer-Verlag, New York, Berlin, Heidelberg, 1971. Zbl0219.46042MR442701
  35. [35] S. Schlieder, Einige Bemerkungen über Projektionsoperatoren. Commun. Math. Phys., t. 13, 1969, p. 216-225. Zbl0179.58001MR250617
  36. [36] R. Schrader, A Yukawa quantum field theory in two spacetime dimensions without cutoffs. Ann. Phys., t. 70, 1972, p. 412-457. MR302088
  37. [37] R.F. Streater and A.S. Wightman, PCT, Spin and Statistics, And All That, New York, Benjamin, 1964. Zbl0135.44305MR161603
  38. [38] S.J. Summers, Normal product states for fermions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa2 quantum field model. Commun. Math. Phys., t. 86, 1982, p. 111-141. Zbl0505.46051MR678005
  39. [39] S.J. Summers and R. Werner, The vacuum violates Bell's inequalities. Phys. Lett., t. 110 A, 1985, p. 257-259. MR803854
  40. [40] S.J. Summers and R. Werner, Bell's inequalities and quantum field theory, I. General setting. J. Math. Phys., t. 28, 1987, p. 2440-2447. Zbl0648.46066MR908015
  41. [41] S.J. Summers and R. Werner, Bell's inequalities and quantum field theory, II. Bell's inequalities are maximally violated in the vacuum. J. Math. Phys., t. 28, 1987, p.2448-2456. Zbl0648.46067MR908016
  42. [42] S.J. Summers and R. Werner, Maximal violation of Bell's inequalities is generic in quantum field theory. Commun. Math. Phys., t. 110, 1987, p. 247-259. Zbl0626.46056MR887998
  43. [43] M. Takesaki, Theory of Operator Algebras, I. Springer-Verlag, New York, Berlin, Heidelberg, 1979. Zbl0436.46043
  44. [44] M. Takesaki, Conditional expectations in von Neumann algebras. J. Funct. Anal., t. 9, 1972, p. 306-321. Zbl0245.46089MR303307
  45. [45] D. Testard, Asymptotic ratio set of von Neumann algebras generated by temperature states in statistical mechanics. Rep. Math. Phys., t. 12, 1977, p. 115-118. Zbl0385.46039MR468970
  46. [46] R. Werner, Local preparability of states and the split property in quantum field theory. Lett. Math. Phys., t. 13, 1987, p. 325-329. Zbl0649.46063MR895295
  47. [47] A.S. Wightman, La théorie quantique locale et la théorie quantique des champs. Ann. Inst. Henri Poincaré, t. A1, 1964, p. 403-420. Zbl0128.45803MR197086

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.