The Hadamard condition for Dirac fields and adiabatic states on Robertson-Walker spacetimes

Communications in Mathematical Physics

Volumn 216, Issue 3, 2001, Pages 635-661

  Hollands, Stefan ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035529590     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200000350     Document Type: Article

References (37)

1. 1. Brunetti, R. and Fredenhagen, K.: Microlocal analysis and interacting quantum field theories: Renormalisation on physical backgrounds. Commun. Math. Phys. 208, 623-661 (2000)
2. 2. Camporesi, R. and Higuchi, A.: On the eigenfunctions of the Dirac operator on spheres and real hyperbolic-spaces. J. Geom. Phys. 20, 1-18 (1996)
3. 3. Dencker, N.: On the propagation of Polarisation Sets for Systems of Real Principal Type. J. Funct. Anal. 46, 351-372 (1982)
4. 4. Dimock, J.: Dirac quantum fields on a manifold. Trans. Am. Math. Soc. 269, 133-147 (1982)
5. 5. Fewster, C.J.: A general worldline quantum inequality. Class. Quant. Grav. 17, 1897-1911 (2000)
6. 6. Friedlaender, F.G.: The Wave Equation on Curved Space-Time. Cambridge: Cambridge University Press, 1975
7. 7. 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. 136, 243-272 (1981)
8. 8. Gonnella, G., Kay, B.S.: Can locally Hadamard quantum states have nonlocal singularities? Class. Quant. Grav. 6, 1445 (1989)
9. 9. Günther, P.: Huygens principle and hyperbolic equations. New York: Academic Press, 1988
10. 10. Haag, R.: Local quantum physics: Fields, particles, algebras. Berlin: Springer-Verlag, 1992
11. 11. Haag, R. and Kastler, D.: An Algebraic Approach to Quantum Field Theory. J. Math. Phys. 5, 848-861 (1964)
12. 12. Haag, R., Narnhofer, H. and Stein, U.: On Quantum Field Theory in Gravitational Background. Commun. Math. Phys. 94, 219-238 (1984)
13. 13. Hörmander, L.: Fourier integral operators. I. Acta Math. 127, 79-183 (1971); Duislermaat, J.J. and Hörmander, L.: Fourier integral operators. II. Acta Math. 128, 183-269 (1972)
14. 13. Hörmander, L.: Fourier integral operators. I. Acta Math. 127, 79-183 (1971); Duislermaat, J.J. and Hörmander, L.: Fourier integral operators. II. Acta Math. 128, 183-269 (1972)
15. 14. Hörmander, L.: The Analysis of Linear Partial Differential Operators. III. Berlin: Springer Verlag, 1985
16. 15. Junker, W.: Hadamard states, adiabatic vacua and the construction of physical states for scalar quantum fields on curved space-time. Rev. Math. Phys. 8, 1091-1159 (1996)
17. 16. Junker, W.: Erratum. In preparation
18. 17. Hollands, S.: PhD thesis, University of York. In preparation
19. 18. Kay. B.S. and 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)
20. 19. Köhler, M.: The stress-energy tensor of a locally supersymmetric quantum field on a curved space-time. PhD thesis, Hamburg, 1995
21. 20. Kratzen, K.: Singularitätsstruktur der Zweipunktfunktion des freien Diracfeldes in einer global hyperbolischen Raumzeit. DESY-THESIS-1999-020, Hamburg, 1999
22. 21. Kratzen, K.: Singularity structure of the twopoint function of a free Dirac field on a globally hyperbolic spacetime. math-pn/0003015, to be published in Annalen der Physik
23. 22. Lüders, C. and Roberts, J.E.: Local quasiequivalence and adiabatic vacuum states. Commun. Math. Phys. 134, 29 (1990)
24. 23. Moretti, W.: Proof of the symmetry of the off-diagonal heat kernel and Hadamards expansion coefficients in general ∞ Riemannian manifolds. gr-qc/9902034
25. 24. Najmi, A., Ottewil, A.: Quantum states and the Hadamard form. II: Energy Minimisation for spin 1/2 Fields. Phys. Rev. D 30, 2573-2584 (1984)
26. 25. Parker, L.: Quantized fields and particle creation in expanding universes. I. Phys. Rev. 183, 1057-1083 (1969)
27. 26. Powers, R.T. and Størmer, E.: Free states of the canonical anticommutation relations. Commun. Math. Phys. 16, 1 (1970)
28. 27. Radzikowski, M.J.: Micro-Local Approach to the Hadamard condition in QFT on Curved Space-Time. Commun. Math. Phys. 179, 529-553 (1996)
29. 28. Radzikowski, M.J.: A local to global singularity theorem for quantum field theory in curved space. Commun. Math. Phys. 180, 1-22 (1996)
30. 29. Radzikowski, M.J.: Unpublished notes
31. 30. Taylor, M.E.: Pseudodifferential Operators. Princeton, NJ: Princeton University Press, 1981; Partial Differential Equations II. Berlin: Springer Verlag, 1996
32. 30. Taylor, M.E.: Pseudodifferential Operators. Princeton, NJ: Princeton University Press, 1981; Partial Differential Equations II. Berlin: Springer Verlag, 1996
33. 31. Trautman, A.: Spin structures on hypersurfaces and the spectrum of the Dirac operator on spheres. In: Spinors Twistors, Clifford Algebras and Quantum Deformations, Dordrecht: Kluwer Academic Publishers, 1993
34. 32. Verch, R.: Local definiteness, primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime. Commun. Math. Phys. 160, 507-536 (1994)
35. 33. Verch, R.: Scaling Analysis and Ultraviolet Behaviour of Quantum Field Theories in Curved Spacetimes. PhD thesis, Hamburg 1996
36. 34. Wald, R.M.: Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Chicago: The University of Chicago Press, 1994
37. 35. Wellmann, M.: Adiabatic vacuum states for the Dirac field on a curved spacetime. hep-th/9802087