Abstract
We show that in Oeckl’s boundary formalism the boundary vectors that do not have a tensor form represent, in a precise sense, statistical states. Therefore the formalism incorporates quantum statistical mechanics naturally. We formulate general-covariant quantum statistical mechanics in this language. We illustrate the formalism by showing how it accounts for the Unruh effect. We observe that the distinction between pure and mixed states weakens in the general covariant context, suggesting that local gravitational processes are naturally statistical without a sharp quantal versus probabilistic distinction.
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Notes
Such a quantum equivalence principle could be a consequence of the dynamics (the Wheeler–deWitt equation) or hold only for states that are semiclassical in an appropriate sense. We do not investigate this question here. Notice that in a field theory on a fixed metric spacetime, a state lacking correlations across a boundary would yield infinite energy density, but presumably this is not so in quantum gravity, because of the Planck scale finiteness (or, equivalently, the finiteness of the Bekenstein entropy). We thank an anonymous referee for this interesting observation.
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Acknowledgements
EB acknowledges support from a Banting Postdoctoral Fellowship from NSERC. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research & Innovation. HMH acknowledges support from the National Science Foundation (NSF) International Research Fellowship Program (IRFP) under Grant No. OISE-1159218.
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Bianchi, E., Haggard, H.M. & Rovelli, C. The boundary is mixed. Gen Relativ Gravit 49, 100 (2017). https://doi.org/10.1007/s10714-017-2263-2
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DOI: https://doi.org/10.1007/s10714-017-2263-2