A quantum weak energy inequality¶for dirac fields in curved spacetime

Communications in Mathematical Physics

Volumn 225, Issue 2, 2002, Pages 331-359

  Fewster, Christopher J ^a   Verch, Rainer ^b  

^a UNIVERSITY OF YORK   (United Kingdom)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001294440     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100584     Document Type: Article

References (50)

1. Araki, H.: On quasifree states of CAR and Bogoliubov transformations. Publ. RIMS 6, 385 (1970/71)
2. Brunetti, R., Fredenhagen, K.: Microlocal analysis and interacting quantum field theories: renormalization on physical backgrounds. Commun. Math. Phys. 208, 623 (2000)
3. Davies, P.C.W., Fulling, S.A.: Radiation from moving mirrors and from black holes. Proc. Roy. Soc. A356, 237 (1977)
4. Deser, S.: Improvement versus stability in gravity-scalar coupling. Phys. Lett. 134B, 419 (1984)
5. Dimock, J.: Dirac quantum fields on a manifold. Trans. Am. Math. Soc. 269, 133 (1982)
6. Epstein, H., Glaser, V., Jaffe, A.: Nonpositivity of the energy density in quantized field theories. Nuovo Cimento 36, 1016 (1965)
7. Fewster, C.J., Eveson, S.P.: Bounds on negative energy densities in flat spacetime. Phys. Rev. D 58, 084010 (1998)
8. Fewster, C.J.: A general worldline quantum inequality. Class. Quantum Grav. 17, 1897 (2000)
9. Fewster, C.J., Teo, E.: Bounds on negative energy densities in static spacetimes. Phys. Rev. D 59, 104016 (1999)
10. Fewster, C.J., Teo, E.: Quantum inequalities and quantum interest as eigenvalue problems. Phys. Rev. D 61, 084012 (2000)
11. Flanagan, É.É.: Quantum inequalities in two-dimensional Minkowski spacetime. Phys. Rev. D 56, 4922 (1997)
12. Flanagan, É.É., Wald, R.M.: Does backreaction enforce the averaged null energy condition in semiclassical gravity? Phys. Rev. D 54, 6233 (1996)
13. Folacci, A.: Averaged-null-energy condition for electromagnetism in Minkowski spacetime. Phys. Rev. D 46, 2726 (1992)
14. Ford, L.H.: Quantum coherence effects and the second law of thermodyamics. Proc. Roy. Soc. Lond. A364, 227 (1978)
15. Ford, L.H., Roman, T.A.: Averaged energy conditions and quantum inequalities. Phys. Rev. D 51, 4277 (1995)
16. Ford, L.H., Roman, T.A.: Restrictions on negative energy density in flat spacetime. Phys. Rev. D 55, 2082 (1997)
17. Ford, L.H., Roman, T.A.: Classical Scalar Fields and the Generalized Second Law. Phys. Rev. D 64, 024023 (2001)
18. Ford, L.H., Roman, T.A.: Quantum field theory constrains traversable wormhole geometries. Phys. Rev. D 53, 5496 (1996)
19. 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)
20. Glaeser, G.: Racine carrée d'une fonction différentiable. Ann. Inst. Fourier, Grenoble 13, 203 (1963)
21. Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge: Cambridge University Press, 1973
22. Helfer, A.D.: The Hamiltonians of Linear Quantum Fields: II. Classically Positive Hamiltonians. arXiv:hep-th/9908012
23. Hollands, S.: The Hadamard condition for Dirac fields and adiabatic states on Robertson-Walker space-times. Commun. Math. Phys. 216, 635 (2001)
24. Hörmander, L.: The analysis of linear partial differential operators I. Berlin: Springer-Verlag, 1983
25. Hörmander, L.: Fourier integral operators. I. Acta Math. 127, 79 (1971)
26. Klinkhammer, G.: Averaged energy conditions for free scalar fields in flat space-time. Phys. Rev. D 43, 2542 (1991)
27. Keyl, M.: Quantum fields on timelike curves. arXiv:math-ph/0012024
28. Köhler, M.: The stress energy tensor of a locally supersymmetric quantum field on a curved spacetime. Dissertation, Hamburg University, 1995. Preprint DESY-95-080, arXiv:gr-qc/9505014
29. Kratzert, K.: Singularity structure of the two-point function of the free Dirac field on a globally hyperbolic spacetime. Annalen Phys. 9, 475 (2000)
30. Najmi, A.-H., Ottewill, A.C.: Quantum states and the Hadamard form II, Energy minimization for spin 1/2 fields. Phys. Rev. D 30, 2573 (1984)
31. Pfenning, M.J.: Quantum inequality restrictions on negative energy densities in curved spacetimes. Ph.D. thesis, Tufts University, 1998. Preprint arXiv:gr-qc/9805037
32. Pfenning, M.J.: Quantum inequalities for the electromagnetic field. Phys. Rev. D 65, 024009 (2002)
33. Pfenning, M.J., Ford, L.H.: The unphysical nature of "warp drive". Class. Quantum Grav. 14, 1743 (1997)
34. Pfenning, M.J., Ford, L.H.: Scalar field quantum inequalities in static spacetimes. Phys. Rev. D 57, 3489 (1998)
35. Radzikowski, M.J.: Micro-local approach to the Hadamard condition in quantum field theory in curved spacetime. Commun. Math. Phys. 179, 529 (1996)
36. Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. III. San Diego: Academic Press, 1979
37. Sahlmann, H., Verch, R.: Passivity and microlocal spectrum condition. Commun. Math. Phys. 214, 705 (2000)
38. Sahlmann, H., Verch, R. : Microlocal spectrum condition and Hadamard form for vector-valued quantum fields in curved spacetime. Rev. Math. Phys. 13, 1203 (2001)
39. Schoen, R., Yau, S.-T: Proof of the positive mass theorem. II.. Commun. Math. Phys. 79, 231 (1981)
40. Taylor, M.E.: Pseudodifferential operators. Princeton: Princeton University Press, 1981
41. Tipler, F.J.: Energy conditions and spacetime singularities. Phys. Rev. D 17, 2521 (1978)
42. Verch, R.: The averaged null energy condition for general quantum field theories in two dimensions. J. Math. Phys. 41, 206 (2000)
43. Visser, M., Barcelo, C: Energy conditions and their cosmological implications. arXiv:gr-qc/0001099
44. Vollick, D.N.: Negative energy density states for the Dirac field in flat space-time. Phys. Rev. D 57, 3484 (1998)
45. Vollick, D.N.: Quantum inequalities in curved two dimensional spacetime. Phys. Rev. D 61, 084022 (2000)
46. Wald, R.M., Yurtsever, U.: General proof of the averaged null energy condition for a massless scalar field in two-dimensional curved spacetime. Phys. Rev. D 44, 403 (1991)
47. Weinless, M.: Existence and uniqueness of the vacuum for linear quantized fields. J. Funct. Anal. 4, 350 (1969)
48. Witten, E.: A new proof of the positive energy theorem. Commun. Math. Phys. 80, 381 (1981)
49. Yurtsever, U.: Averaged null energy condition and difference inequalities in quantum field theory. Phys. Rev. D 51, 5797 (1995)
50. Yurtsever, U.: Remarks on the averaged null energy condition in quantum field theory. Phys. Rev. D 52, R564 (1995)