Entanglement entropy for non-coplanar regions in quantum field theory

TL;DR

This paper investigates entanglement entropy for non-coplanar regions in relativistic quantum field theory using a real-time approach, revealing relativistic effects like boost enhancement and implications for black hole radiation.

Contribution

It introduces a real-time method to compute entanglement entropy for non-coplanar regions, highlighting relativistic effects not accessible via Euclidean techniques.

Findings

Boosts significantly enhance entanglement entropy.

Mutual information remains non-zero at zero volume with high boost.

Entropy exhibits extensivity in strongly Lorentzian regimes.

Abstract

We study the entanglement entropy in a relativistic quantum field theory for regions which are not included in a single spatial hyperplane. This geometric configuration cannot be treated with the Euclidean time method and the replica trick. Instead, we use a real time method to calculate the entropy for a massive free Dirac field in two dimensions in some approximations. We find some specifically relativistic features of the entropy. First, there is a large enhancement of entanglement due to boosts. As a result, the mutual information between relatively boosted regions does not vanish in the limit of zero volume and large relative boost. We also find extensivity of the information in a deeply Lorentzian regime with large violations of the triangle inequalities for the distances. This last effect is relevant to an interpretation of the amount of entropy enclosed in the Hawking radiation emitted by a black hole.