Decoherent Histories of Spin Networks

Abstract

The decoherent histories formalism, developed by Griffiths, Gell-Mann, and Hartle (in Phys. Rev. A 76:022104, 2007; arXiv:1106.0767v3 [quant-ph], 2011; Consistent Quantum Theory, Cambridge University Press, 2003; arXiv:gr-qc/9304006v2, 1992) is a general framework in which to formulate a timeless, ‘generalised’ quantum theory and extract predictions from it. Recent advances in spin foam models allow for loop gravity to be cast in this framework. In this paper, I propose a decoherence functional for loop gravity and interpret existing results (Bianchi et al. in Phys. Rev. D 83:104015, 2011; Phys. Rev. D 82:084035, 2010) as showing that coarse grained histories follow quasiclassical trajectories in the appropriate limit.

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Fig. 1

Notes

  1. 1.

    See [28] for a description of this formalism.

  2. 2.

    Notwithstanding Savvidou [30].

  3. 3.

    In the following, I only consider the case where the cosmological constant is zero. The non-vanishing case is largely similar; details can be found in [2].

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Acknowledgements

I am indebted to my supervisor Carlo Rovelli, without whom this work would not have been possible. In addition, I would like to thank James Yearsley, Jonathan Halliwell, Edward Anderson, Petros Wallden, Kinjalk Lochan, Ed Wilson-Ewing, Simone Speziale, Aldo Riello, Wolfgang Wieland, as well as Leonard Cottrell for helpful comments and discussions. I am supported by the German National Academic Foundation (Studienstiftung des deutschen Volkes).

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Correspondence to David P. B. Schroeren.

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Schroeren, D.P.B. Decoherent Histories of Spin Networks. Found Phys 43, 310–328 (2013). https://doi.org/10.1007/s10701-013-9698-4

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Keywords

  • Decoherent histories
  • Class operator
  • Decoherence functional
  • Spin network
  • Quantum gravity
  • Spin foams
  • Path integral
  • Coarse graining
  • Probability