Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Infravacua and the Localisation of Sectors

Walter Kunhardt

TL;DR

The paper investigates localization of a class of infrared-charged sectors for the free massless scalar field in 3+1 dimensions. It shows that these sectors fail BF localization in the vacuum but can achieve better localization, in spacelike cones, relative to infravacuum backgrounds modeled after Kraus–Polley–Reents. By constructing KPR-like quasifree infravacua, the authors prove an explicit intertwining mechanism that restores cone-local equivalence of sectors in the infravacuum setting, while preserving energy positivity and superselection structure. The results illuminate how infrared clouds influence superselection and enable a DHR-like analysis in non-Lorentz-invariant backgrounds, albeit with some limitations on full BF localisation across all cones.

Abstract

A certain class of superselection sectors of the free massless scalar field in 3 space dimensions is considered. It is shown that these sectors, which cannot be localised with respect to the vacuum, acquire a much better localisation, namely in spacelike cones, when viewed in front of suitable ``infravacuum'' backgrounds. These background states coincide, essentially, with a class of states introduced by Kraus, Polley and Reents as models for clouds of infrared radiation.

On Infravacua and the Localisation of Sectors

TL;DR

The paper investigates localization of a class of infrared-charged sectors for the free massless scalar field in 3+1 dimensions. It shows that these sectors fail BF localization in the vacuum but can achieve better localization, in spacelike cones, relative to infravacuum backgrounds modeled after Kraus–Polley–Reents. By constructing KPR-like quasifree infravacua, the authors prove an explicit intertwining mechanism that restores cone-local equivalence of sectors in the infravacuum setting, while preserving energy positivity and superselection structure. The results illuminate how infrared clouds influence superselection and enable a DHR-like analysis in non-Lorentz-invariant backgrounds, albeit with some limitations on full BF localisation across all cones.

Abstract

A certain class of superselection sectors of the free massless scalar field in 3 space dimensions is considered. It is shown that these sectors, which cannot be localised with respect to the vacuum, acquire a much better localisation, namely in spacelike cones, when viewed in front of suitable ``infravacuum'' backgrounds. These background states coincide, essentially, with a class of states introduced by Kraus, Polley and Reents as models for clouds of infrared radiation.

Paper Structure

This paper contains 8 sections, 12 theorems, 39 equations.

Table of Contents

  1. Introduction
  2. Bad localisation of the sectors in front of the vacuum
  3. Infravacuum background states
  4. Preliminaries on quasifree states
  5. Quasifree states with positive energy
  6. KPR-like quasifree states
  7. Better localisation of the sectors in front of KPR-like infravacua
  8. Conclusions

Key Result

Proposition 2.1

Let $C\subset\mathbb{R}^3$ be an open convex cone having $0$ as its apex and denote with ${\cal{C}}\hbox{,{\rm :}$=$,} (\{0\}\times C)"$ its causal completion. Then, for any $\gamma\in {\cal{L}}_\Gamma$,

Theorems & Definitions (12)

  • Proposition 2.1
  • Lemma 2.2
  • Lemma 3.1
  • Lemma 3.2
  • Lemma 3.3
  • Proposition 3.4
  • Lemma 3.5
  • Lemma 3.6
  • Proposition 4.1
  • Lemma 4.2
  • ...and 2 more