Geometric modular action and transformation groups
Annales de l'I.H.P. Physique théorique, Volume 64 (1996) no. 4, pp. 409-432.
@article{AIHPA_1996__64_4_409_0,
     author = {Summers, Stephen J.},
     title = {Geometric modular action and transformation groups},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {409--432},
     publisher = {Gauthier-Villars},
     volume = {64},
     number = {4},
     year = {1996},
     mrnumber = {1407754},
     zbl = {0860.46054},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1996__64_4_409_0/}
}
TY  - JOUR
AU  - Summers, Stephen J.
TI  - Geometric modular action and transformation groups
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1996
SP  - 409
EP  - 432
VL  - 64
IS  - 4
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1996__64_4_409_0/
LA  - en
ID  - AIHPA_1996__64_4_409_0
ER  - 
%0 Journal Article
%A Summers, Stephen J.
%T Geometric modular action and transformation groups
%J Annales de l'I.H.P. Physique théorique
%D 1996
%P 409-432
%V 64
%N 4
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1996__64_4_409_0/
%G en
%F AIHPA_1996__64_4_409_0
Summers, Stephen J. Geometric modular action and transformation groups. Annales de l'I.H.P. Physique théorique, Volume 64 (1996) no. 4, pp. 409-432. http://archive.numdam.org/item/AIHPA_1996__64_4_409_0/

[1] A.D. Alexandrov, On Lorentz transformations, Uspehi Mat. Nauk., Vol. 5, 1950, pp. 187.

[2] H. Araki, Symmetries in theory of local observables and the choice of the net of local algebras, Rev. Math. Phys., Special Issue, 1992, pp. 1-14. | MR | Zbl

[3] U. Bannier, Intrinsic algebraic characterization of space-time structure, Int. J. Theor. Phys., Vol. 33, 1994, pp. 1797-1809. | MR | Zbl

[4] J. Bisognano and E.H. Wichmann, On the duality condition for a hermitian scalar field, J. Math. Phys., Vol. 16, 1975, pp. 985-1007. | MR | Zbl

[5] H.-J. Borchers and G.C. Hegerfeldt, The structure of space-time transformations, Commun. Math. Phys., Vol. 28, 1972, pp. 259-266. | MR | Zbl

[6] H.-J. Borchers, The PCT-theorem in two-dimensional theories of local observables, Commun. Math. Phys., Vol. 143, 1992, pp. 315-332. | MR | Zbl

[7] O. Bratteli and D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics I, Berlin, Heidelberg, New York: Springer-Verlag, 1979. | MR | Zbl

[8] R. Brunetti, D. Guido and R. Longo, Group cohomology, modular theory and space-time symmetries, Rev. Math. Phys., Vol. 7, 1995, pp. 57-71. | MR | Zbl

[9] D. Buchholz and S.J. Summers, An algebraic characterization of vacuum states in Minkowski space, Commun. Math. Phys., Vol. 155, 1993, pp. 449-458. | MR | Zbl

[10] D. Buchholz, O. Dreyer and S.J. Summers, work in progress.

[11] K. Fredenhagen, Global observables in local quantum physics, in: Quantum and Non-Commutative Analysis, Amsterdam: Kluwer Academic Publishers, 1993. | MR | Zbl

[12] K. Fredenhagen, Quantum field theories on nontrivial spacetimes, in: Mathematical Physics Towards the 21st Century, ed. by R. N. Sen and A. Gersten, Beer-Sheva: Ben-Gurion University Negev Press, 1993.

[13] D. Guido, Modular covariance, PCT, Spin and Statistics, Ann. Inst. Henri Poincaré, Vol. 63, 1995, pp. 383-398. | Numdam | MR | Zbl

[14] D. Guido and R. Longo, An algebraic spin and statistics theorem, I, to appear in Commun. Math. Phys. | MR

[15] P.D. Hislop and R. Longo, Modular structure of the local algebras associated with the free massless scalar field theory, Commun. Math. Phys., Vol. 84, 1982, pp. 71-85. | MR | Zbl

[16] M. Keyl, Causal spaces, causal complements and their relations to quantum field theory, to appear in Rev. Math. Phys. | MR | Zbl

[17] B. Kuckert, A new approach to spin & statistics, Lett. Math. Phys., Vol. 35, 1995, pp. 319-331. | Zbl

[18] J.A. Lester, Separation-preserving transformations of De Sitter spacetime, Abh. Math. Sem. Univ. Hamburg, Vol. 53, 1983, pp. 217-224. | MR | Zbl

[19] G. Mackey, Les ensembles Boréliens et les extensions des groupes, J. Math. Pures Appl., Vol. 36, 1957, pp. 171-178. | MR | Zbl

[20] C.C. Moore, Group extensions and cohomology for locally compact groups, IV, Trans. Amer. Math. Soc., Vol. 221, 1976, pp. 35-58. | MR | Zbl

[21] J.E. Roberts and G. Roepstorff, Some basic concepts of algebraic quantum theory, Commun. Math. Phys., Vol. 11, 1969, pp. 321-338. | MR | Zbl

[22] H.-W. Wiesbrock, A comment on a recent work of Borchers, Lett. Math. Phys., Vol. 25, 1992, pp. 157-159. | MR | Zbl

[23] H.-W. Wiesbrock, Conformal quantum field theory and half-sided modular inclusions of von Neumann algebras, Commun. Math. Phys., Vol. 158, 1993, pp. 537-543. | MR | Zbl

[24] M. Wollenberg, On the relation between a conformal structure in spacetime and nets of local algebras of observables, Lett. Math. Phys., Vol. 31, 1994, pp. 195-203. | MR | Zbl

[25] E.C. Zeeman, Causality implies the Lorentz group, J. Math. Phys., Vol. 5, 1964, pp. 490-493. | MR | Zbl

[26] R.J. Zimmer, Ergodic Theory and Semisimple Groups, Boston, Basel and Stuttgart: Birkhäuser, 1984. | MR | Zbl