Microlocal analysis of quantum fields on curved space-times: Analytic wave front sets and Reeh-Schlieder theorems

Journal of Mathematical Physics

Volumn 43, Issue 11, 2002, Pages 5514-5530

  Strohmaier, Alexander ^a   Verch, Rainer ^b   Wollenberg, Manfred ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036849071     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1506381     Document Type: Article

References (55)

1. H. Reeh and S. Schlieder, Nuovo Cimento 22, 1051 (1961).
2. R. Haag, Local Quantum Physics: Fields, Particles, Algebras (Springer, Berlin, 1992).
3. R.F. Streater and A.S. Wightman, PCT, Spin and Statistics, and all that, 2nd ed. (Addison-Wesley, Reading, MA, 1989).
4. H. Baumgärtel and M. Wollenberg, Causal Nets of Operator Algebras: Mathematical Aspects of Algebraic Quantum Field Theory (Akademie-Verlag, Berlin, 1992).
5. C.D' Antoni, "Technical properties of the quasilocal algebra," in Proceedings of the Algebraic Theory of Superselection Sectors Palermo, 1989, edited by D. Kastler (World Scientific, Singapore, 1990), pp. 248-258.
6. C.D. Jäkel, J. Math. Phys. 41, 1745 (2000).
7. R. Verch, Lett. Math. Phys. 28, 143 (1993).
8. A. Strohmaier, Commun. Math. Phys. 215, 105 (2000).
9. C. Bär and A. Strohmaier, Diff. Geom. Applic. 15, 175 (2001).
10. J.E. Roberts, "Lectures on algebraic quantum field theory," In Proceedings of The Algebraic Theory of Superselection Sectors, Palermo, 1989, edited by D. Kastler (World Scientific, Singapore, 1990), pp. 1-112.
11. M. Takesaki, Tomita's Theory of Modular Hilbert Algebras and its Applications, Lecture Notes in Mathematics Vol. 128 (Springer, Berlin, 1970).
12. J.J. Bisognano and E.H. Wichmann, J. Math. Phys. 16, 985 (1975).
13. J.J. Bisognano and E.H. Wichmann, J. Math. Phys. 17, 303 (1976).
14. H.J. Borchers, J. Math. Phys. 41, 3604 (2000).
15. D. Buchholz, O. Dreyer, M. Florig, and S.J. Summers, Rev. Math. Phys. 12, 475 (2000).
16. D. Buchholz, J. Mund, and S.J. Summers, Fields Inst. Commun. 30, 65 (2001).
17. S.J. Summers and R. Werner, Ann. I.H.P. Phys. Theor. 49, 215 (1988).
18. H. Halvorson and R. Clifton, J. Math. Phys. 41, 1711 (2000).
19. C.D. Jäkel, Found. Phys. Lett. 14, 1 (2001).
20. R. Verch and R.F. Werner (unpublished).
21. S.J. Summers, Rev. Math. Phys. 2, 201 (1990).
22. D. Beckman, D. Gottesman, M.A. Nielsen, and J. Preskill, Phys. Rev. A 64, 052309 (2001).
23. R.M. Wald, Gen. Relativ. Gravit. 24, 1111 (1992).
24. M.J. Radzikowski, Ph.D. thesis, Princeton University, 1992.
25. M.J. Radzikowski, Commun. Math. Phys. 179, 529 (1996).
26. K. Kratzert, Ann. Phys. (Leipzig) 9, 475 (2000).
27. S. Hollands, Commun. Math. Phys. 216, 635 (2001).
28. H. Sahlmann and R. Verch, Rev. Math. Phys. 13, 1203 (2001).
29. R.M. Wald, Commun. Math. Phys. 54, 1 (1977).
30. R. Brunetti, K. Fredenhagen, and M. Köhler, Commun. Math. Phys. 180, 633 (1996).
31. R. Brunetti and K. Fredenhagen, Commun. Math. Phys. 208, 623 (2000).
32. S. Hollands and R. Wald, Commun. Math. Phys. 223, 289 (2001).
33. L. Hörmander, The Analysis of Linear Partial Differential Operators. I (Springer, New York, 1990).
34. R.M. Wald, General Relativity (Chicago University Press, Chicago, 1984).
35. S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-time (Cambridge University Press, Cambridge, 1973).
36. J. Leray, Hyperbolic Differential Equations, Mimeographed Notes (Institute of Advanced Study, Princeton, 1955).
37. J. Dimock, Commun. Math. Phys. 77, 219 (1980).
38. S.A. Fulling, Aspects of Quantum Field Theory in Curved Space-time (Cambridge University Press, Cambridge, 1989).
39. B.S. Kay and R.M. Wald, Phys. Rep. 207, 49 (1991).
40. R.M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (Chicago University Press, Chicago, 1994).
41. L. Hörmander, Acta Math. 127, 79 (1971).
42. J.J. Duistermaat and L. Hörmander, Acta Math. 128, 183 (1972).
43. S. Hollands and R.M. Wald, "Existence of local covariant time ordered products of quantum fields in curved space-time," gr-qc/0111108.
44. R. Verch, Commun. Math. Phys. 160, 507 (1994).
45. S.A. Fulling, F.J. Narcowich, and R.M. Wald, Ann. Phys. (N.Y.) 136, 243 (1981).
46. H. Sahlmann and R. Verch, Commun. Math. Phys. 214, 705 (2000).
47. W. Junker and E. Schrohe, "Adiabatic vacuum states on general space-time manifolds: Definition, construction, and physical properties," math-ph/0109010.
48. J. Bros and D. Buchholz, Nucl. Phys. B 429, 291 (1994).
49. J. Bros and D. Buchholz, Ann. I.H.P. Phys. Theor. 64, 495 (1996).
50. J. Bros and U. Moschella, Rev. Math. Phys. 8, 327 (1996).
51. J. Bros, H. Epstein, and U. Moschella, Commun. Math. Phys. 196, 535 (1998).
52. J. Bros, H. Epstein, and U. Moschella, Phys. Rev. D 65, 084012 (2002).
53. G.W. Gibbons and S.W. Hawking, Phys. Rev. D 15, 2738 (1977).
54. J. Bros and U. Moschella, Rev. Math. Phys. 8, 327 (1996).
55. W. Junker, Rev. Math. Phys. 8, 1091 (1996).