Deconfinement in d=1: A closer look

TL;DR

This paper re-examines deconfinement phenomena in one-dimensional models, exploring the relationship between different types of excitations and their implications for higher-dimensional theories.

Contribution

It provides a detailed analysis of the connection between asymptotic and half-asymptotic particles in 1D models, clarifying their relationship and potential relevance to higher dimensions.

Findings

Half-asymptotic and truly asymptotic particles are related by complex transformations.

Both the Schwinger model and Heisenberg chain exhibit these two types of excitations.

Insights may inform understanding of deconfinement in higher-dimensional systems.

Abstract

The notion of deconfinement in two d=1 models, the Schwinger model and the Heisenberg chain, is re-examined. Both have half-asymptotic excitations (where particles and antiparticles must alternate) and also truly asymptotic particles which are half as many in number. The two kinds of particles are related by a complicated transformation. The main purpose of this note is to highlight the relationship between asymptotic and half-asymptotic particles. The relevance of our findings to higher dimensions is briefly discussed.