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Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory

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Book cover Special Relativity

Part of the book series: Lecture Notes in Physics ((LNP,volume 702))

Abstract

A summary of some lines of ideas leading to model-independent frameworks of relativistic quantum field theory is given. It is followed by a discussion of the Reeh-Schlieder theorem and geometric modular action of Tomita-Takesaki modular objects associated with the quantum field vacuum state and certain algebras of observables. The distillability concept, which is significant in specifying useful entanglement in quantum information theory, is discussed within the setting of general relativistic quantum field theory.

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References

  1. Araki, H, General principles of quantum field theory, Oxford University Press, 1990

    Google Scholar 

  2. Bargmann, V., Ann. Math. 49(1947) 568 & Ann. Math. 59(1954) 1; J. Math. Phys. 5(1964) 862

    Article  MathSciNet  Google Scholar 

  3. Baumgärtel, H., Operatoralgebraic methods in quantum field theory, Akademie Verlag, Berlin, 1995

    MATH  Google Scholar 

  4. Beckman, D., Gottesman, D., Nielsen, M.A., Preskill, J., Phys. Rev. A 64 (2001) 052309

    ADS  Google Scholar 

  5. Bennett, C.H., Brassard, G., Crépeau, C., Josza, R., Peres, A., Wootters, W.K., Phys. Rev. Lett. 70(1993) 1; Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Phys. Rev. Lett. 761996) 722; erratum ibid. 781997) 2031; Gisin, N., Phys. Lett A 2101996) 151

    Article  MathSciNet  Google Scholar 

  6. Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K., Phys.Rev.A 541996) 3824

    Article  MathSciNet  ADS  Google Scholar 

  7. Bisognano, J.J., Wichmann, E.H., J. Math. Phys. 16(1975) 985 & 171976) 303

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. Bogoliubov N.N., Lugonov, A.A., Oksak A.I., Todorov, I.T., General principles of quantum field theory, Kluwer, Dordrecht, 1990

    Google Scholar 

  9. Borchers, H.-J., J. Math. Phys. 412000) 3604

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. Borchers, H.-J., Nuovo Cimento 151960) 784

    Article  MATH  MathSciNet  Google Scholar 

  11. Bratteli, O., Robinson, D.W., Operator algebras and quantum statistical mechanics, Vol. 1, 2nd ed., Springer, Berlin-Heidelberg-New York, 1987

    Google Scholar 

  12. Bratteli, O., Robinson, D.W., Operator algebras and quantum statistical mechanics, Vol. 2, 2nd ed., Springer, Berlin-Heidelberg-New York, 1997

    Google Scholar 

  13. Bros, J., Buchholz, D., Nucl. Phys. B429, 2911994)

    Article  MathSciNet  ADS  Google Scholar 

  14. Buchholz, D., Lechner, G., Ann. H. Poincaré 52004) 1065

    Article  MATH  Google Scholar 

  15. Buchholz, D., Mund, J., Summers, S.J., Fields Inst. Commun. 302001) 65

    MATH  MathSciNet  Google Scholar 

  16. Buchholz, D., Wichmann, E.H., Commun. Math. Phys. 1061986) 321

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. Buchholz, D., Yngvason, J., Phys. Rev. Lett. 731994) 613

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. Cirel’son, B.S., Lett. Math. Phys. 4, 931980).

    Article  MathSciNet  ADS  Google Scholar 

  19. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A., Phys. Rev. Lett. 261969) 8801969)

    Google Scholar 

  20. Dixmier, J., Maréchal, O., Commun. Math. Phys. 221971) 44

    Article  MATH  ADS  Google Scholar 

  21. Doplicher, S., Roberts, J.E., Commun. Math. Phys. 1311990) 51

    Article  MATH  MathSciNet  ADS  Google Scholar 

  22. Eggeling, T., Schlingemann, D., Werner, R.F., Europhys. Lett. 57, 7822001)

    Article  ADS  Google Scholar 

  23. Ekert, A.K., Phys. Rev. Lett. 67, 6611991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  24. Fewster, C.J., “Energy inequalities in quantum field theory”, math-ph/0501073

    Google Scholar 

  25. Fulling, S.A., Phys. Rev. D71973) 2850

    ADS  Google Scholar 

  26. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H., Rev. Mod Phys. 742002) 145; A. Poppe et al., “Practical quantum key distribution with polarization entangled photons”, quant-ph/0404115; Jennewein, T., Ursin, R., Aspelmeyer, M., Zeilinger, A., “Experimental teleportation of quantum entanglement with an optimal linear optics Bell-state analyzer”, quant-ph/0409008; Jennewein, T., Weihs, G., Pan, J.-W., Zeilinger, A., Phys. Rev. Lett 882002) 017903; Weihs, G., Jennewein, T., Simon, C., Weinfurter, H., Zeilinger, A., Phys. Rev. Lett 811998) 5039

    Article  ADS  Google Scholar 

  27. Glimm, J., Jaffe, A., Quantum physics, Springer-Verlag, New York, 1987

    MATH  Google Scholar 

  28. Haag, R., Local quantum physics, Springer-Verlag, Berlin, 1992

    MATH  Google Scholar 

  29. Haag, R., Kastler, D., J. Math. Phys. 51964) 848

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. Haag, R., Hugenholtz, N.M., Winnink, M., Commun. Math. Phys. 51967) 215

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. Halvorson, H., Clifton, R., J. Math. Phys. 412000) 1711

    Article  MATH  MathSciNet  ADS  Google Scholar 

  32. Hellwig, K.-E., Kraus, K., Phys. Rev. D11970) 566 & Commun. Math. Phys. 161970) 142

    ADS  Google Scholar 

  33. Henley, E.M., Thirring, W., Elementary quantum field theory, McGraw-Hill, New York, 1962

    MATH  Google Scholar 

  34. Itzykson, C., Zuber, Quantum field theory, McGraw-Hill, Singapore, 1985

    Google Scholar 

  35. Jäkel, C.D., J. Math. Phys. 412000) 1745

    Article  MATH  MathSciNet  ADS  Google Scholar 

  36. Jäkel, C.D., Found. Phys. Lett. 142001) 1

    Article  MathSciNet  Google Scholar 

  37. Jost, R., The general theory of quantum fields, AMS, Providence, 1965

    Google Scholar 

  38. Kähler, R., Wiesbrock, H.-W., J. Math. Phys. 422001) 74

    Article  MATH  MathSciNet  ADS  Google Scholar 

  39. Keyl, M., Schlingemann, D., Werner, R.F., Quant. Inf. Comp. 32003) 281

    MathSciNet  MATH  Google Scholar 

  40. Keyl, M., Phys. Rep. 3692002) 431

    Article  MATH  MathSciNet  ADS  Google Scholar 

  41. Kraus, K., States, effects and operations, Springer Lecture Notes in Physics, Springer-Verlag, Berlin, 1972

    Google Scholar 

  42. Landau, L.J., Phys. Lett. A1201987) 54

    ADS  Google Scholar 

  43. Landau, L.J., Phys. Lett. A1231987) 115

    ADS  Google Scholar 

  44. Montvay, I., Münster, G., Quantum fields on a lattice, Cambridge University Press, 1994

    Google Scholar 

  45. Pais, A., Subtle is the Lord. The science and life of Albert Einstein, Oxford University Press, 1982

    Google Scholar 

  46. Peres, A., Quantum theory: concepts and methods, Kluwer, Dordrecht, 1993

    MATH  Google Scholar 

  47. Peres, A., Terno, D.R., Rev. Mod. Phys. 762004) 93

    Article  MathSciNet  ADS  Google Scholar 

  48. Popescu, S., Phys. Rev. Lett. 741995) 2619

    Article  MATH  MathSciNet  ADS  Google Scholar 

  49. Reed, C., Simon, B., Methods of mathematical physics, Vol. II, Academic Press, New York, 1975

    Google Scholar 

  50. Reeh, H., Schlieder, S., Nuovo Cimento 221961) 1051

    Article  MathSciNet  Google Scholar 

  51. Rehren, K.-H., Commun. Math. Phys. 1781996) 453

    Article  MATH  MathSciNet  ADS  Google Scholar 

  52. Reznik, B., Retzker, A., Silman, J., Phys. Lett. A3372005) 17

    Google Scholar 

  53. Rivasseau, V., From perturbative to constructive renormalization, Princeton University Press, 1991

    Google Scholar 

  54. Roberts, J.E., More lectures on algebraic quantum field theory, in: S. Doplicher and R. LongoEds.), Springer Lecture Notes in Mathematics 1831, pp. 263–342, Springer-Verlag, Berlin 2004

    Google Scholar 

  55. Roberts, J.E., Roepstorff, G., Commun. Math. Phys. 111968) 321

    Article  MathSciNet  ADS  Google Scholar 

  56. Schlieder, S., Commun. Math. Phys. 71968) 305

    Article  MATH  ADS  MathSciNet  Google Scholar 

  57. Schroer, B., Wiesbrock, H.-W., Rev. Math. Phys. 122000) 301

    Article  MATH  MathSciNet  Google Scholar 

  58. Sewell, G.L., Ann. Phys. 1411982) 201

    Article  MathSciNet  ADS  Google Scholar 

  59. Sexl, R.U., Urbantke, H.K., Relativity, groups, particles, Springer-Verlag, Wien, 2001

    MATH  Google Scholar 

  60. Streater, R.F., Wightman, A.S., PCT, spin and statistics, and all that, Benjamin, New York, 1964

    MATH  Google Scholar 

  61. Summers, S.J., Verch, R., Lett. Math. Phys, 371996) 145

    Article  MATH  MathSciNet  ADS  Google Scholar 

  62. Summers S.J., Werner, R.F., Lett. Math. Phys. 331995) 321 ; – Ann. Inst. H. Poincaré 491988) 215; – Commun. Math. Phys. 1101987) 247; - Phys. Lett. A 1101985) 257

    Article  MATH  MathSciNet  ADS  Google Scholar 

  63. Summers, S.J., Werner, R.F., J. Math. Phys. 281987) 2448

    Article  MATH  MathSciNet  ADS  Google Scholar 

  64. Summers, S.J., Rev. Math. Phys. 21990) 201

    Article  MATH  MathSciNet  Google Scholar 

  65. Takesaki, M., Tomita’s theory of modular Hilbert algebras and its applications Springer Lecture Notes in Mathematics 128, Springer-Verlag, Berlin, 1970

    Google Scholar 

  66. Unruh, W.G., Phys. Rev. D141976) 870

    ADS  Google Scholar 

  67. Verch, R., Werner, R.F., Rev. Math. Phys. 172005) 545–576

    Article  MATH  MathSciNet  Google Scholar 

  68. Weinberg, S., The quantum theory of fields, Vols. I-III, Cambridge University Press, 1996–2000

    Google Scholar 

  69. Wheeler, J.A., Zurek, W.H.Eds.), Quantum theory and measurement, Princeton University Press, 1983

    Google Scholar 

  70. Wigner, E.P., Ann. math. 401939) 149

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Leipzig Postfach 10 09 20, Leipzig, 04009, Germany

    R. Verch

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  1. R. Verch
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Editors and Affiliations

  1. Albert-Einstein-Institut MPl Gravitationsphysik, Am Mühlenberg 1, Golm, 14476, Germany

    Jürgen Ehlers

  2. ZARM, Universität Bremen Am Fallturm, Bremen, 28359, Germany

    Claus Lämmerzahl

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Verch, R. (2006). Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory. In: Ehlers, J., Lämmerzahl, C. (eds) Special Relativity. Lecture Notes in Physics, vol 702. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34523-X_6

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