Probabilities and signalling in quantum field theory

Article, Preprint English OPEN
Dickinson, Robert ; Forshaw, Jeff ; Millington, Peter (2016)
  • Publisher: American Physical Society
  • Related identifiers: doi: 10.1103/PhysRevD.93.065054
  • Subject: High Energy Physics - Phenomenology | Mathematical Physics | High Energy Physics - Theory | Quantum Physics

We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anti-commutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anti-commutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.
  • References (8)

    appreciated [16{18]. A noteable exception to this was Hegerfeldt's 1994 paper [19], which

    created quite a media stir [20, 21] and provoked the clarifying response in [22]. [5] S. Kikuchi, Z. Phys. 66, 558 (1930). [6] B. Ferretti and R. E. Peierls, Nature (London) 160, 531 (1947), Letters to the Editors. [7] W. Heitler and S. T. Ma, Proc. R. Ir. Acad. 52, 109 (1949). [8] J. Hamilton, Proc. Phys. Soc. London Sect. A 62, 12 (1949). [9] B. Ferretti, in Old and New Problems in Elementary Particles, edited by G. Puppi (Academic

    Press, New York, 1968) p. 108. [10] M. I. Shirokov, Sov. Phys. Usp. 21, 345 (1978). [11] W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973) p. 314. [12] P. W. Milonni and P. L. Knight, Phys. Rev. A10, 1096 (1974). [13] M. H. Rubin, Phys. Rev. D35, 3836 (1987). [14] A. K. Biswas, G. Compagno, G. M. Palma, R. Passante, and F. Persico, Phys. Rev. A42,

    4291 (1990), Erratum: Phys. Rev. A44, 798 (1991). [15] A. Valentini, Phys. Lett. A153, 321 (1991). [16] E. A. Power and T. Thirunamachandran, Phys. Rev. A56, 3395 (1997). [17] P. W. Milonni, D. F. V. James, and H. Fearn, Phys. Rev. A52, 1525 (1995). [18] I. Dolce, R. Passante, and F. Persico, Phys. Lett. A355, 152 (2006). [19] G. C. Hegerfeldt, Phys. Rev. Lett. 72, 596 (1994). [20] J. Maddox, Nature (London) 367, 509 (1994), News and Views. [21] J. Gribbin, New Scientist 1914, 16 (1994). [22] D. Buchholz and J. Yngvason, Phys. Rev. Lett. 73, 613 (1994), arXiv:hep-th/9403027 [hep-th]. [23] S. Schlieder, in Quanten und Felder, edited by H. Durr (Vieweg und Sohn, Verlag, Braun-

    schweig, 1971) p. 145. [24] H. Neumann and R. Werner, Int. J. Theo. Phys. 22, 781 (1983). [25] G. C. Hegerfeldt, Ann. Phys. (Berlin) 7, 716 (1998), arXiv:quant-ph/9809030 [quant-ph]. [26] M. Cliche and A. Kempf, Phys. Rev. A81, 012330 (2010), arXiv:0908.3144 [quant-ph]. [27] E. Mart n-Mart nez, Phys. Rev. D92, 104019 (2015), arXiv:1509.07864 [quant-ph]. [28] J. D. Franson and M. M. Donegan, Phys. Rev. A 65, 052107 (2002), quant-ph/0108018. [29] R. Dickinson, J. Forshaw, P. Millington, and B. Cox, JHEP 06, 049 (2014), arXiv:1312.3871

    [hep-th]. [30] D. Hummer, E. Mart n-Mart nez, and A. Kempf, Phys. Rev. D93, 024019 (2016),

    arXiv:1506.02046 [quant-ph]. [31] J. S. Schwinger, J. Math. Phys. 2, 407 (1961). [32] L. V. Keldysh, Zh. Eksp. Teor. Fiz. 47, 1515 (1964), [Sov. Phys. JETP20,1018(1965)]. [33] R. L. Kobes and G. W. Semeno , Nucl. Phys. B260, 714 (1985). [34] R. L. Kobes and G. W. Semeno , Nucl. Phys. B272, 329 (1986). [35] Cutkosky, R. E., J. Math. Phys. 1, 429 (1960). [36] G. 't Hooft and M. J. G. Veltman, 2nd Summer Institute on Particle Interactions at Very

    Sci. Ser. B 4, 177 (1974). [37] R. Kobes, Phys. Rev. D43, 1269 (1991).

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