Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II (The search of the interface between QFT and QG)

TL;DR

This paper explores the implications of vacuum polarization in quantum field theory and quantum gravity, revealing new approaches to localization, entropy behavior near horizons, and symmetry structures including BMS groups.

Contribution

It introduces a novel outside-inwards constructive approach based on modular localization and analyzes the holographic symmetry enhancements involving BMS groups.

Findings

Vacuum polarization leads to a new localization approach.

Localization entropy near horizons follows a modified area law.

Holographic projections reveal infinite-dimensional symmetry groups including BMS.

Abstract

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive "outside-inwards approach" in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior. Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi-Metzner-Sachs group.