On the Lattice of Subalgebras Associated with the Principle of Half-sided Modular Inclusion

Letters in Mathematical Physics

Volumn 40, Issue 4, 1997, Pages 371-390

  Borchers, H J ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Modular groups; Modular inclusion; Quantum field theory

Indexed keywords

EID: 0039417320     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007396816791     Document Type: Article

References (22)

1. D'Antoni, C. D., Doplicher, S., Fredenhagen, K. and Longo, R.: Convergence of local charges and continuity properties of W*-inclusions, Comm. Math. Phys. 110 (1987), 325-398.
2. Borchers, H.-J.: Translation Group and Particle Representations in Quantum Field Theory, Lecture Notes in Physics 40, Springer-Verlag, Berlin, Heidelberg, New York, 1996.
3. Borchers, H.-J.: Über die Vollständigkeit lorentzinvarianter Felder in einer zeitartigen Röhre, Nuovo Cim. 19 (1961), 787-796.
4. Borchers, H.-J.: The CPT-theorem in two-dimensional theories of local observables, Comm Math. Phys. 143 (1992), 315-332.
5. Borchers, H.-J.: On modular inclusion and spectrum condition, Lett. Math. Phys. 27 (1993) 311-324.
6. Borchers, H.-J.: Half-sided modular inclusion and the construction of the Poincaré group, Comm. Math. Phys. 179 (1996), 703-723.
7. Bratteli, O. and Robinson, D. W.: Operator Algebras and Quantum Statistical Mechanics I, Springer-Verlag, New York, Heidelberg, Berlin, 1979.
8. Bremermann, H. J., Oehme, R. and Taylor, J. G.: Proof of dispersion relation in quantized field theories, Phys. Rev. 109 (1958), 2178-2190.
9. Bros, J., Epstein, H., Glaser, V. et Stora, R.: Quelques aspects globaux des problemes d'edge-of-the-wedge, in: Hyperfunctions and Theoretical Physics (Nice Rencontre 1973), Lecture Notes in Math. 449, Springer-Verlag, Berlin, Heidelberg, New York, 1975.
10. Buchholz, D.: On the structure of local quantum fields with non-trivial interactions, in: Proc. Internat. Conf. on Operator Algebras, Ideals and their Applications in Theoretical Physics, Leipzig, 1977, Teubner-Texte zur Mathematik, 1978, pp. 146-153.
11. Chernoff, P.: Product formulas, non-linear semigroups, and addition of unbounded operators, Mem. Amer. Math. Soc. 140 (1974).
12. Connes, A.: Caractérisation des algèbres de von Neumann comme espaces vectoriels ordonnés, Ann. Inst. Fourier (Grenoble) 24 (1974), 121-155.
13. Kadison, R. V. and Ringrose, J. R.: Fundamentals of the Theory of Operator Algebras II, Academic Press, New York, 1986.
14. Nussbaum, A. E.: Reduction theory for unbounded closed operators in Hubert space, Duke Math. J. 31 (1964), 33-44.
15. Pedersen, G. K.: C*-Algebras and their Automorphism Groups, Academic Press, London, New York, San Francisco, 1979.
16. Riesz, F. and Nagy, B.: Vorlesungen über Funktionalanalysis, Deutscher Verlag der Wissenschaften, Berlin, 1973.
17. Stone, M. H.: On unbounded operators in Hilbert space, J. Indiana Math. Soc. 15 (1951).
18. Takesaki, M.: Tomita's Theory of Modular Hilbert Algebras and its Applications, Lecture Notes in Math. 128, Springer-Verlag Berlin, Heidelberg, New York, 1970.
19. Vladimirov, V. S.: The construction of envelopes of holomorphy for domains of special type, Dokla. Akad. Nauk SSSR 134 (1960), 251.
20. Wiesbrock, H.-W.: Symmetries and half-sided modular inclusions of von Neumann algebras, Lett. Math. Phys. 28 (1993), 107-114.
21. Wiesbrock, H.-W.: Conformal quantum field theory and half-sided modular inclusions of von Neumann algebras, Comm. Math. Phys. 158 (1993), 537-543.
22. Wiesbrock, H.-W: Modular intersections of von Neumann algebras in quantum field theory, in preparation.