References
Bisognano, J., Wichmann, E.H.: On the duality for a hermitian scalar field. J. Math. Phys.16, 985–1007 (1975)
Borchers, H.-J.: On the converse of, the Reeh-Schlieder theorem. Commun. Math. Phys.10, 269–273 (1968)
Brehmermann, H.J., Oehme, R., Taylor, J.D.: Proof of dispersion relation in quantized field theories. Phys. Rev.109, 2178–2190 (1958)
Buchholz, D., D'Antoni, C., Longo, R.: Nuclear maps and modular structure. II. Applications to quantum field theory. Commun. Math. Phys.129, 115–138 (1990)
Buchholz, D., and Junglas, P.: On the existence of equilibrium states in local quantum field theory. Commun. Math. Phys.121, 255–270 (1989)
Buchholz, D., Wichman, E.H.: Causal independence and the energy level density of states in local quantum field theory. Commun. Math. Phys.106, 321–344 (1986)
Fredenhagen, K.: On the modular structure of local algebras of observables. Commun. Math. Phys.97, 79–89 (1985)
Hislop, P.D., Longo, R.: Modular structure of the local algebra associated with a free massless scalar field theory. Commun. Math. Phys.84, 71–85 (1982)
Reeh, H., Schlieder, S.: Bemerkungen zur Unitäräquivalenz von Lorentzinvarianten Feldern. Il Nuovo Cimento22, 1051–1068 (1961)
Takesaki, M.: Tomita's theory of modular Hilbert algebras and its applications, Lecture Notes in Mathematics. Berlin, Heidelberg, New York: Springer 1970
Tomita, M.: Standard forms of von Neumann algebras. Fifth functional analysis symposium of Math. Soc. of Japan, Sendai
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Dedicated to Res Jost and Arthur Wightman
Rights and permissions
About this article
Cite this article
Borchers, H.J. Translation group and modular automorphisms for local regions. Commun.Math. Phys. 132, 189–199 (1990). https://doi.org/10.1007/BF02278007
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02278007