Abstract
The entanglement harvesting protocol developed in Chap. 3 is applied to detectors in Minkowski space and two cylindrical spacetimes constructed by topological identifications of Minkowski space. To do so, the image sum derivation of the Wightman functions in these cylindrical spacetimes is presented. It is shown that the entanglement harvesting protocol depends sensitively on the global topology of these spacetimes, suggesting that the entanglement structure of a field theory is sensitive to the global spacetime topology in such a way that is in principle observable by detectors interacting locally with the field.
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Notes
- 1.
In this chapter, we will simply say ‘vacuum state’ without explicitly stating the vacuum state agreed on by all inertial observers.
- 2.
\( \lim _{\epsilon \to 0} \frac {1}{x\pm i \epsilon } = \mp i \pi \delta (x) + \operatorname {\mathrm {PV}} \frac {1}{x}\).
- 3.
A smooth function that tends to zero as y →±∞.
- 4.
One might imagine a Michelson-Morley-Bell experiment in which a large number of pairs of atoms in a cavity interact with the electromagnetic vacuum and become entangled. From these atoms, entanglement is distilled and used to violate a Bell inequality. Perhaps, one would find that the success of violating a Bell inequality would depend on the orientation of the atoms with respect to the cavity walls.
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Smith, A.R.H. (2019). Unruh-DeWitt Detectors in Quotients of Minkowski Space. In: Detectors, Reference Frames, and Time. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-11000-0_4
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DOI: https://doi.org/10.1007/978-3-030-11000-0_4
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