Target space entanglement entropy
Abstract We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worl...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2023
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| Online Access: | https://hdl.handle.net/1721.1/148624 |
| Summary: | Abstract
We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to each subregion of the target space a suitably chosen subalgebra of observables
A
$$ \mathcal{A} $$
. The entanglement entropy is calculated as the entropy of the density matrix restricted to
A
$$ \mathcal{A} $$
. As an example, we illustrate our framework by computing spatial entanglement in first-quantized many-body quantum mechanics. The algebra
A
$$ \mathcal{A} $$
is chosen to reproduce the entanglement entropy obtained by embedding the state in the fixed particle sub-sector of the second-quantized Hilbert space. We then generalize our construction to the quantum field-theoretical setting. |
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