@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://www.numdam.org/item/AIHPA_1996__64_4_409_0/} }
Summers, Stephen J. Geometric modular action and transformation groups. Annales de l'I.H.P. Physique théorique, Tome 64 (1996) no. 4, pp. 409-432. http://www.numdam.org/item/AIHPA_1996__64_4_409_0/
[1] On Lorentz transformations, Uspehi Mat. Nauk., Vol. 5, 1950, pp. 187.
,[2] 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] Intrinsic algebraic characterization of space-time structure, Int. J. Theor. Phys., Vol. 33, 1994, pp. 1797-1809. | MR | Zbl
,[4] On the duality condition for a hermitian scalar field, J. Math. Phys., Vol. 16, 1975, pp. 985-1007. | MR | Zbl
and ,[5] The structure of space-time transformations, Commun. Math. Phys., Vol. 28, 1972, pp. 259-266. | MR | Zbl
and ,[6] The PCT-theorem in two-dimensional theories of local observables, Commun. Math. Phys., Vol. 143, 1992, pp. 315-332. | MR | Zbl
,[7] Operator Algebras and Quantum Statistical Mechanics I, Berlin, Heidelberg, New York: Springer-Verlag, 1979. | MR | Zbl
and ,[8] Group cohomology, modular theory and space-time symmetries, Rev. Math. Phys., Vol. 7, 1995, pp. 57-71. | MR | Zbl
, and ,[9] An algebraic characterization of vacuum states in Minkowski space, Commun. Math. Phys., Vol. 155, 1993, pp. 449-458. | MR | Zbl
and ,[10] work in progress.
, and ,[11] Global observables in local quantum physics, in: Quantum and Non-Commutative Analysis, Amsterdam: Kluwer Academic Publishers, 1993. | MR | Zbl
,[12] 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] Modular covariance, PCT, Spin and Statistics, Ann. Inst. Henri Poincaré, Vol. 63, 1995, pp. 383-398. | Numdam | MR | Zbl
,[14] An algebraic spin and statistics theorem, I, to appear in Commun. Math. Phys. | MR
and ,[15] 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
and ,[16] Causal spaces, causal complements and their relations to quantum field theory, to appear in Rev. Math. Phys. | MR | Zbl
,[17] A new approach to spin & statistics, Lett. Math. Phys., Vol. 35, 1995, pp. 319-331. | Zbl
,[18] Separation-preserving transformations of De Sitter spacetime, Abh. Math. Sem. Univ. Hamburg, Vol. 53, 1983, pp. 217-224. | MR | Zbl
,[19] Les ensembles Boréliens et les extensions des groupes, J. Math. Pures Appl., Vol. 36, 1957, pp. 171-178. | MR | Zbl
,[20] Group extensions and cohomology for locally compact groups, IV, Trans. Amer. Math. Soc., Vol. 221, 1976, pp. 35-58. | MR | Zbl
,[21] Some basic concepts of algebraic quantum theory, Commun. Math. Phys., Vol. 11, 1969, pp. 321-338. | MR | Zbl
and ,[22] A comment on a recent work of Borchers, Lett. Math. Phys., Vol. 25, 1992, pp. 157-159. | MR | Zbl
,[23] 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] 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] Causality implies the Lorentz group, J. Math. Phys., Vol. 5, 1964, pp. 490-493. | MR | Zbl
,[26] Ergodic Theory and Semisimple Groups, Boston, Basel and Stuttgart: Birkhäuser, 1984. | MR | Zbl
,