The generally covariant locality principle - A new paradigm for local quantum field theory

Communications in Mathematical Physics

Volumn 237, Issue 1-2, 2003, Pages 31-68

  Brunetti, Romeo ^a   Fredenhagen, Klaus ^a   Verch, Rainer ^b  

^a UNIVERSITY OF HAMBURG   (Germany)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037972693     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0815-7     Document Type: Article

References (53)

1. Araki, H.: Mathematical theory of quantum fields. Oxford: Oxford University Press, 1999
2. Atiyah, M.: Topological quantum field theories. Publ. Math. IHES Paris 68, 178 (1989)
3. Bannier, U.: On generally covariant quantum field theory and generalized causal and dynamical structures. Commun. Math. Phys 118, 163 (1988)
4. Horchers, H.J.: On the structure of the algebra of field operators. Nuovo Cimento 24, 214 (1962)
5. Bratteli, O., Robinson, D.W.: Operator algebras and quantum statistical mechanics. Vol. 1, 2nd ed., Berlin: Springer-Verlag, 1987
6. Brunetti, R., Fredenhagen, K.: Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds. Commun. Math. Phys. 208, 623 (2000)
7. Brunetti, R., Fredenhagen, K., Köhler, M.: The microlocal spectrum condition and Wick polynomials on curved spacetime. Commun. Math. Phys. 180, 633 (1996)
8. Buchholz, D.: Product states for local algebras. Commun. Math. Phys. 36, 287 (1974)
9. Buchholz, D., Wichmann, E.H.: Causal independence and the energy-level density of states in quantum field theory. Commun. Math. Phys. 106, 321 (1986)
10. Dieudonné, J.: Foundations of modern analysis. Vol. 3, New York: Academic Press, 1972
11. Dimock, J.: Algebras of local observables on a manifold. Commun. Math. Phys. 77, 219 (1980)
12. Dimock, J.: Dirac quantum fields on a manifold. Trans. Am. Math. Soc. 269, 133 (1982)
13. Dixmier, J.: Les C*-algèbres et leurs représentations. Paris: Gauthier-Villars, 1964
14. Dosch, H.G., Müller, V.F.: Renormalization of quantum electrodynamics in an arbitrarily strong time-independent external field. Fortsch. Phys. 23, 661 (1975)
15. Dütsch, M., Fredenhagen, K.: Algebraic quantum field theory, perturbation theory, and the loop expansion. Commun. Math. Phys. 219, 5 (2001); Perturbative algebraic field theory and deformation quantization. Fields Inst. Commun. 30, 151 (2001)
16. Dütsch, M., Fredenhagen, K.: Algebraic quantum field theory, perturbation theory, and the loop expansion. Commun. Math. Phys. 219, 5 (2001); Perturbative algebraic field theory and deformation quantization. Fields Inst. Commun. 30, 151 (2001)
17. Dyson, F.J.: Missed opportunities. Bull. Am. Math. Soc. 78, 635 (1972)
18. Fewster, C.J., Verch, R.: Passivity from quantum weak energy inequalities. Preprint, math-ph/0203010 (to appear in Commun. Math. Phys.)
19. Fredenhagen, K., Haag, R.: Generally covariant quantum field theory and scaling limits. Commun. Math. Phys. 108, 91 (1987)
20. Fulling, S.A.: Non-uniqueness of canonical field quantization in Riemannian space-time. Phys. Rev. D 7, 2850 (1973)
21. Fulling, S.A., Narcowich, F.J., Wald, R.M.: Singularity structure of the two-point function in quantum field theory in curved spacetime, II. Ann. Phys. (N.Y.) 136, 243 (1981)
22. Haag, R.: Local Quantum Physics. 2nd ed. Berlin, Heidelberg, New York: Springer-Verlag, 1996
23. Haag, R., Narnhofer, H., Stein, U.: On quantum field theories in gravitational background. Commun. Math. Phys. 94, 219 (1984)
24. Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys. 5, 848 (1964)
25. Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)
26. Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge: Cambridge University Press, 1973
27. Hollands, S., Wald, R.M.: Local Wick polynomials and time ordered products of quantum fields in curved spacetime. Commun. Math. Phys 223, 289 (2001)
28. Hollands, S., Wald, R.M.: Existence of local covariant time ordered products of quantum fields in curved spacetime. Commun. Math. Phys. 231, 309 (2002)
29. Hörmander, L.: The analysis of partial differential operators. Vol 1. Berlin-Heidelberg-New York: Springer-Verlag, 1983
30. Kay, B.S.: Quantum fields in curved spacetime: Non global hyperbolicity and locality. In: The Proceedings of the Conference Operator Algebras and Quantum Field Theory Held in Rome, July 1996, S. Doplicher, R. Longo, J.E. Roberts, L. Zsido (eds.), Cambridge MA: International Press, 1997
31. Kay, B.S.: Linear spin-0 quantum fields in external gravitational and scalar fields, II. Commun. Math. Phys. 71, 29 (1980)
32. Kay, B.S., Wald, R.M.: Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasifree states on spacetimes with a bifurcate Killing horizon. Phys. Rep. 207, 49 (1991)
33. Mac Lane, S.: Categories for the working mathematician. New York: Springer-Verlag, 1971
34. Moretti, V.: Comments on the stress-energy operator in curved spacetime. Commun. Math. Phys. 232, 189 (2003)
35. Norton, J.D.: The hole argument. Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/spacetime-holearg
36. Ojima, I.: Quantum-Field Theoretical Approach to Non-Equilibrium Dynamics in Curved Space-Time. Proc. 2nd Int. Symp. Foundations of Quantum Mechanics, Tokyo 1986, pp. 91-96
37. Radzikowski, M.J.: Micro-local approach to the Hadamard condition in quantum field theory in curved spacetime. Commun. Math. Phys. 179, 529 (1996)
38. Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. 2, Orlando: Academic Press, 1975
39. Sahlmann, H., Verch, R.: Passivity and microlocal spectrum condition. Commun. Math. Phys. 214, 705 (2000)
40. Sahlmann, H., Verch, R.: Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime. Rev. Math. Phys. 13, 1203 (2001)
41. 2 quantum field model. Commun. Math. Phys. 86, 111 (1982)
42. Summers, S.J.: On the independence of local algebras in quantum field theory. Rev. Math. Phys. 2, 201 (1990)
43. Torre, C.G., Varadarajan, M.: Functional evolution of free quantum fields. Class. Quantum Grav 16, 2651 (1999)
44. Uhlmann, A.: Über die Definition der Quantenfelder nach Wightman und Haag. Wiss. Zeits. Karl Marx Univ. Leipzig 11, 213 (1962)
45. Verch, R.: Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime. Commun. Math. Phys. 160, 507 (1994)
46. Verch, R.: Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime. Rev. Math. Phys. 9, 635 (1997)
47. Verch, R.: Wavefront sets in algebraic quantum field theory. Commun. Math. Phys. 205, 337 (1999)
48. Verch, R.: A spin-statistics theorem for quantum fields on curved spacetime manifolds in a generally covariant framework. Commun. Math. Phys. 223, 261 (2001)
49. Unruh, W.G.: Notes on black hole evaporation. Phys. Rev. D 14, 870 (1976)
50. Wald, R.M.: The back reaction effect in particle creation in curved spacetime. Commun. Math. Phys. 54, 1 (1977)
51. Wald, R.M.: Existence of the S-matrix in quantum field theory in curved spacetime. Ann. Phys. (N.Y.) 118, 490 (1979)
52. Wald, R.M.: General relativity, Chicago: University of Chicago Press, 1984
53. Wald, R.M.: Quantum field theory in curved spacetime and black hole thermodynamics. Chicago: University of Chicago Press, 1994