Mass Dependence of the Araki-Uhlmann Relative Entropy Across Dimensions

TL;DR

This paper analyzes how the Araki-Uhlmann relative entropy between a localized excitation and vacuum in a free scalar quantum field varies with mass and dimension, revealing complex behaviors through analytical and numerical methods.

Contribution

It extends previous 1+1 dimensional analyses of relative entropy to higher dimensions, providing new insights into its dependence on mass and spacetime dimensionality.

Findings

Relative entropy's analytic structure depends on mass and dimension.

Numerical results show non-monotonic behavior in higher dimensions.

The study offers new understanding of quantum field theoretic entropy measures.

Abstract

We investigate the mass dependence of the Araki-Uhlmann relative entropy between a localized coherent excitation and the vacuum state of a free scalar quantum field on the $(1+d)$-dimensional Minkowski spacetime for $d = 1, 2, 3$. In this context, the relative entropy admits a closed expression in terms of the smeared Pauli-Jordan distribution, whose analytic structure is sensitive to both the mass and the spacetime dimensionality. Prior studies in $(1+1)$ dimensions have shown a monotonic decay of the relative entropy with increasing mass. We extend that analysis to higher dimensions using numerical techniques and elucidate how the interplay between dimensionality and mass controls the behavior of the relative entropy. Our results provide new insights for the study of the Araki-Uhlmann relative entropy in QFT and its dependence on physical parameters.