# Entropy of Coherent Excitations

## TL;DR

This paper derives an explicit formula for the vacuum relative entropy of coherent states in wedge-localized von Neumann algebras within free quantum field theories, accounting for charges on the time-zero hyperplane.

## Contribution

It provides a rigorous and explicit expression for vacuum relative entropy in wedge-localized algebras for free quantum fields, including boundary-crossing charges.

## Key findings

- Explicit formula for vacuum relative entropy derived
- Applicable to arbitrary spacetime dimensions
- Includes charges crossing the boundary on the hyperplane

## Abstract

We provide a rigorous, explicit formula for the vacuum relative entropy of a coherent state on wedge local von Neumann algebras associated with a free, neutral quantum field theory on the Minkowski spacetime of arbitrary spacetime dimension. We consider charges localised on the time zero hyperplane, possibly crossing the boundary.