Abstract
It is proved for a Haag–Araki–Kastler quantum field theory, that gravitation reduces the correlations in the vacuum state. Secondly, we prove Bell's inequalities by nuclearity assumptions. The so-called ε-content of certain compact mappings restricts the size of the set of measurements which violate Bell's inequalities.
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References
Summers, S. J. and Werner, R. F.: On Bell's inequalities and algebraic invariants, Lett. Math. Phys. 33(4) (1995) 321–334.
Summers, S. J. and Werner, R. F.: The vacuum violates Bell's inequalities, Phys. Lett. A 110 (1985), 257–259.
Raggio, G. A.: A remark on Bell's inequality and decomposable normal states, Lett. Math. Phys. 15 (1988), 27–29.
Wollenberg, M.: Algebras at space-time points for nets of local observables, Preprint, TU Berlin.
Fredenhagen, K.: A remark on the cluster property, Comm. Math. Phys. 97 (1985), 461–464.
Buchholz, D. and Yngvason, Y.: Generalized nuclearity conditions and the split property in quantum field theory, Lett. Math. Phys. 23(2) (1991), 159–167.
Hawking, S. W.: Particle creation by black holes, Comm. Math. Phys. 43 (1975), 199–220.
Summers, S. J. and Verch, R.: Modular inclusion, the Hawking temperature, and quantum field theory in a curved spacetime, Lett. Math. Phys. 37 (1993), 145–158.
Haag, R.: Local Quantum Physics, Springer, New York, 1992.
Penrose, R.: Quantum Concepts of Space and Time, Oxford Sci. Publ. 3, Oxford Univ. Press, 1984.
Buchholz, D. and Wichmann, E. H.: Causal independence and energy level density of states in quantum field theory, Comm. Math. Phys. 106 (1986), 321–343.
Jarchow, H.: Locally Convex Spaces, Teubner, Stuttgart, 1980.
Buchholz, D. and Porrmann, M.: How small is the phase space in quantum field theory? Anal. Inst. H. Poincare 52 (1990), 237–257.
Schumann, R.: Operator ideals and the statistical independence in quantum field theory, Lett. Math. Phys. 27(3) (1996), 159–271.
Buchholz, D., D'Antonio, C. and Longo, R.: Nuclear maps and modular structures I, J. Funct. Anal. 88 (1990), 233.
Haag, R. and Swieca, J. A.:When does a quantum field theory describe particles? Comm. Math. Phys. 1 (1965), 308–320.
Borchers, H. J.: Translation Groups and Particle Representation in Quantum Field Theory, Springer, New York, 1996.
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Schumann, R. Quantum Correlations, Nuclearity, and Spacetime Curvature. Letters in Mathematical Physics 47, 1–17 (1999). https://doi.org/10.1023/A:1007553113988
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DOI: https://doi.org/10.1023/A:1007553113988