Target Space Entanglement in Quantum Mechanics of Fermions and Matrices

TL;DR

This paper introduces the concept of target space entanglement in quantum mechanics, especially for fermions and matrices, using an algebraic approach to define entanglement entropy in contexts where target space relates directly to spacetime.

Contribution

It generalizes the definition of entanglement entropy to target space, applying it to first quantized fermions and matrices, expanding the understanding of entanglement in quantum gravity contexts.

Findings

Defined target space entanglement entropy using algebraic methods

Applied the concept to fermions and matrix models

Provided a framework connecting target space entanglement to spacetime structure

Abstract

Quantum entanglement is closely related to the structure of spacetime in quantum gravity. For quantum field theories or statistical models, we usually consider base space entanglement. However, target space instead of base space sometimes directly connects to our spacetime. In these cases, it is natural to consider a concept of target space entanglement. To define the target space entanglement, we consider a generalized definition of entanglement entropy based on an algebraic approach. This approach is reviewed and is applied to the first quantized particles, in particular, fermions. This article is based on the paper JHEP 08 (2021) 046 [arXiv:2105.13726].