Borchers' Commutation Relations and Modular Symmetries in Quantum Field Theory

Letters in Mathematical Physics

Volumn 41, Issue 4, 1997, Pages 307-320

  Kuckert, Bernd ^a  

^a UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Operator algebras; PCT theorem; Quantum field theory; Spin statistics theorem; Symmetries

Indexed keywords

EID: 0001799589     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007300201901     Document Type: Article

References (35)

1. Araki, H.: A generalization of Borchers' theorem, Helv. Phys. Acta 36 (1963), 132.
2. Araki, H.: Symmetries in a theory of local observables and the choice of the local algebras, Rev. Math Phys., Special Issue (1992), 1-14.
3. Bannier, U.: Intrinsic algebraic charaterization of space-time structure, Internat. J. Theoret. Phys. 33 (1994), 1797-1809.
4. Baumgärtel, H. and Wollenberg, M.: Causal Nets of Operator Algebras, Akademie-Verlag, Berlin, 1992.
5. Bisognano, J. J. and Wichmann, E. H.: On the duality condition for a Hermitean scalar field, J. Math. Phys. 17 (1975), 985-1007.
6. Bisognano, J. J. and Wichmann, E. H.: On the duality condition for quantum fields, J. Math. Phys. 17 (1976), 303.
7. Borchers, H. J.: On the converse of the Reeh-Schlieder theorem, Comm. Math. Phys. 10 (1968), 269-273.
8. Borchers, H. J.: The CPT-theorem in two-dimensional theories of local observables, Comm. Math. Phys. 143 (1992), 315-332.
9. Bratteli, O. and Robinson, D.: Operator Algebras and Quantum Statistical Mechanics I, Springer-Verlag, Berlin, Heidelberg, New York, 1979.
10. Brunetti, R., Guido, D. and Longo, R.: Modular structure and duality in conformal quantum field theory, Comm. Math. Phys. 156 (1993), 201-219.
11. Brunetti, R., Guido, D. and Longo, R.: Group cohomology, modular theory and space-time symmetries, Rev. Math. Phys. 7 (1995), 57-71.
12. Bros, J., Messiah, A. and Stora, R.: A problem of analytic completion related to the Jost-Lehmann-Dyson formula, J. Math Phys. 2 (1961), 639-651.
13. Buchholz, D.: Collision theory for massless fermions, Comm. Math. Phys. 42 (175), 269-279.
14. Buchholz, D.: Collision theory for waves in two dimensions and a characterization of models with trivial S-matrix, Comm. Math. Phys. 45 (1975), 1-8.
15. Buchholz, D.: Collision theory of massless bosons, Comm. Math. Phys. 52 (1977), 147-173.
16. Buchholz D.: On the structure of local quantum fields with non-trivial interaction in: Proc. Internat. Conf. on Operator Algebras, Ideals and Their Applications in Theoretical Physics, Leipzig 1977, Teubner, Stuttgart, 1978.
17. Buchholz, D. and Fredenhagen, K.: Dilations and interaction, J. Math. Phys. 18 (1977), 1107-1111.
18. Buchholz, D. and Fredenhagen, K.: Locality and the structure of particle states, Comm. Math. Phys. 84 (1982), 1-54.
19. Dyson, F. J.: Integral representations of causal commutators, Phys. Rev. 110 (1958), 1460.
20. Fredenhagen, K. and Jörß, M.: Conformal Haag-Kastler nets pointlike localized fields and the existence of operator product expansions, DESY preprint 94-174 October 1994.
21. Gabbiani, F. and Fröhlich, J.: Operator algebras and conformal quantum field theory, Comm. Math. Phys. 155 (1993), 569-640.
22. Guido. D. and Longo, R.: Relativistic invariance and charge conjugation, Comm. Math. Phys. 148 (1992), 521-551.
23. Guido, D. and Longo, R.: An algebraic spin and statistics theorem, Comm. Math. Phys. 172 (1995), 517-534.
24. Guido, D. and Longo, R.: The conformal spin and statistics theorem, Preprint, Rome 1995, hep-th/9505059.
25. Haag, R.: Local Quantum Physics, Springer-Verlag, Berlin Heidelberg, New York, 1992.
26. Jost R. and Lehmann, H.: Integral representation of causal commutators, Nuovo Cim. 5 (1957), 1598-1608.
27. Keyl, M.: Remarks on the relation between causality and quantum fields, Classical Quantum Gravity 10 (1993), 2353-2362.
28. Kuckert, B.: PCT- und Poincarésymmetrie als modulare Strukturen; ein algebraisches Spin-Statistik-Theorem, Diploma thesis, Hamburg, 1994
29. Kuckert B.: A new approach to spin & statistics, Lett. Math. Phys. 35 (1995), 319-335.
30. Kuckert, B.: Joint work with D. Davidson and D. Guido, not yet published.
31. Landau, L. J.: A note on extended locality, Comm. Math. Phys. 13 (1969), 246-253.
32. Takesaki, M.: Tomita 's Theory of Modular Hilbert Algebras and Its Applicanons, Lecture Notes in Math. 128, Springer-Verlag, New York, 1970.
33. Wiesbrock, H.-W.: Conformal quantum field theory and halfsided modular inclusions, Comm. Math. Phys. 158 (1993), 537-544.
34. Yngvason, J.: A note on essential duality, Lett. Math. Phys 31 (1994), 127-141.
35. Zeeman, E. C.: Causality implies the lorentz group, J. Math. Phys. 5 (1964), 490-493.