@article{AIHPA_1989__51_4_419_0, author = {Figliolini, Franca and Guido, Daniele}, title = {The {Tomita} operator for the free scalar field}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {419--435}, publisher = {Gauthier-Villars}, volume = {51}, number = {4}, year = {1989}, mrnumber = {1034596}, zbl = {0715.46049}, language = {en}, url = {http://archive.numdam.org/item/AIHPA_1989__51_4_419_0/} }
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 SP - 419 EP - 435 VL - 51 IS - 4 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPA_1989__51_4_419_0/ LA - en ID - AIHPA_1989__51_4_419_0 ER -
Figliolini, Franca; Guido, Daniele. The Tomita operator for the free scalar field. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 4, pp. 419-435. http://archive.numdam.org/item/AIHPA_1989__51_4_419_0/
[1] A Lattice of von Neumann Algebras Associated with the Quantum Field Theory of a Free Bose Field, J. Math. Phys., Vol. 4, 1963, pp. 1343-1362. | MR | Zbl
,[2] The Local von Neumann Algebras for the Massless Scalar Free Field and the Free Electromagnetic Field, J. Math. Phys., Vol. 19, 1978. | MR
and ,[3] On the Duality Condition for an Hermitian Scalar Field, J. Math. Phys., Vol. 16, 1975, p. 985. | MR | Zbl
and ,[4] Structure of the Algebras of Some Free Systems, Comm. Math. Phys., Vol. 9, 1968, pp.81-117. | MR | Zbl
,[5] An Application of Tomita's Theory of Modular Hilbert Algebras: Duality for Free Bose Field, J. Funct. Analysis, Vol. 13, 1973, pp. 1- 22. | MR | Zbl
and ,[6] The type of Second Quantization Factors, Preprint. | MR
and ,[7] On the Equilibrium States in Quantum Statistical Mechanics, Comm. Math. Phys., Vol. 5, 1967, pp. 215-236. | MR | Zbl
, and ,[8] Modular Structure of the Local Observables Associated with the Free Massless Scalar Field Theory, Comm. Math. Phys., Vol. 84, 1982. | MR | Zbl
and ,[9] Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1984.
,[10] Non-Homogeneous Boundary value problems and applications I, Springer-Verlag, Berlin, 1972. | Zbl
and ,[11] Sobolev Spaces, Springer-Verlag, Berlin, 1985. | MR
,[12] Duality for Quantum Free Fields, unpublished paper.
, and ,[13] Methods of Modern Mathematical Physics, Vol. I and II, Academic Press, 1975.
and ,[14] Anti-Locality of Certain Invariant Operators, J. Math. Mech., Vol. 14, 1965. | Zbl
and ,[15] Relativity of Temperature and Hawking Effect, Phys. Lett., Vol. 79A, 1980, p. 23. | MR
,[16] Causality Implies the Lorentz Group, J. Math. Phys., Vol. 5, 1964. | MR | Zbl
,