Defining entanglement without tensor factoring: a Euclidean hourglass prescription
arXiv:2111.03886 · doi:10.1103/PhysRevD.105.085003
Abstract
We consider entanglement across a planar boundary in flat space. Entanglement entropy is usually thought of as the von Neumann entropy of a reduced density matrix, but it can also be thought of as half the von Neumann entropy of a product of reduced density matrices on the left and right. The latter form allows a natural regulator in which two cones are smoothed into a Euclidean hourglass geometry. Since there is no need to tensor-factor the Hilbert space, the regulated entropy is manifestly gauge-invariant and has a manifest state-counting interpretation. We explore this prescription for scalar fields, where the entropy is insensitive to a non-minimal coupling, and for Maxwell fields, which have the same entropy as scalars.
arXiv comment25 pages. v2: references added. v3: version to appear in PRD
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