The Tomita operator for the free scalar field

Franca Figliolini; Daniele Guido

Annales de l'I.H.P. Physique théorique (1989)

  • Volume: 51, Issue: 4, page 419-435
  • ISSN: 0246-0211

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Figliolini, Franca, and Guido, Daniele. "The Tomita operator for the free scalar field." Annales de l'I.H.P. Physique théorique 51.4 (1989): 419-435. <http://eudml.org/doc/76475>.

@article{Figliolini1989,
author = {Figliolini, Franca, Guido, Daniele},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Tomita operator; local algebra of the free scalar field; second quantization structure of the free fields; time zero formulation},
language = {eng},
number = {4},
pages = {419-435},
publisher = {Gauthier-Villars},
title = {The Tomita operator for the free scalar field},
url = {http://eudml.org/doc/76475},
volume = {51},
year = {1989},
}

TY - JOUR
AU - Figliolini, Franca
AU - Guido, Daniele
TI - The Tomita operator for the free scalar field
JO - Annales de l'I.H.P. Physique théorique
PY - 1989
PB - Gauthier-Villars
VL - 51
IS - 4
SP - 419
EP - 435
LA - eng
KW - Tomita operator; local algebra of the free scalar field; second quantization structure of the free fields; time zero formulation
UR - http://eudml.org/doc/76475
ER -

References

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  2. [2] G. Benfatto and F. Nicolo, The Local von Neumann Algebras for the Massless Scalar Free Field and the Free Electromagnetic Field, J. Math. Phys., Vol. 19, 1978. MR468828
  3. [3] J.J. Bisognano and E.H. Wichmann, On the Duality Condition for an Hermitian Scalar Field, J. Math. Phys., Vol. 16, 1975, p. 985. Zbl0316.46062MR438943
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  5. [5] J.P. Eckmann and K. Osterwalder, An Application of Tomita's Theory of Modular Hilbert Algebras: Duality for Free Bose Field, J. Funct. Analysis, Vol. 13, 1973, pp. 1- 22. Zbl0262.46068MR345548
  6. [6] F. Figliolini and D. Guido, The type of Second Quantization Factors, Preprint. Zbl0847.46042MR1331775
  7. [7] R. Haag, N.M. Hugenoltz and M. Winnik, On the Equilibrium States in Quantum Statistical Mechanics, Comm. Math. Phys., Vol. 5, 1967, pp. 215-236. Zbl0171.47102MR219283
  8. [8] P. Hislop and R. Longo, Modular Structure of the Local Observables Associated with the Free Massless Scalar Field Theory, Comm. Math. Phys., Vol. 84, 1982. Zbl0491.46060MR660540
  9. [9] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1984. 
  10. [10] J.-L. Lions and E. Magenes, Non-Homogeneous Boundary value problems and applications I, Springer-Verlag, Berlin, 1972. Zbl0223.35039
  11. [11] G.V. Maz'ja, Sobolev Spaces, Springer-Verlag, Berlin, 1985. MR817985
  12. [12] J.E. Roberts, P. Leyland and D. Testard, Duality for Quantum Free Fields, unpublished paper. 
  13. [13] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. I and II, Academic Press, 1975. Zbl0308.47002
  14. [14] Segal and Goodman, Anti-Locality of Certain Invariant Operators, J. Math. Mech., Vol. 14, 1965. Zbl0151.44201
  15. [15] G.L. Sewell, Relativity of Temperature and Hawking Effect, Phys. Lett., Vol. 79A, 1980, p. 23. MR597629
  16. [16] E.C. Zeeman, Causality Implies the Lorentz Group, J. Math. Phys., Vol. 5, 1964. Zbl0133.23205MR162587

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