Infraparticles with Superselected Direction of Motion in Two-Dimensional Conformal Field Theory

Wojciech Dybalski,Yoh Tanimoto

doi:10.1007/s00220-012-1450-y

Abstract

Particle aspects of two-dimensional conformal field theories are investigated, using methods from algebraic quantum field theory. The results include asymptotic completeness in terms of (counterparts of) Wigner particles in any vacuum representation and the existence of (counterparts of) infraparticles in any charged irreducible product representation of a given chiral conformal field theory. Moreover, an interesting interplay between the infraparticle’s direction of motion and the superselection structure is demonstrated in a large class of examples. This phenomenon resembles the electron’s momentum superselection expected in quantum electrodynamics.

Highlights

Particle aspects and superselection structure of quantum electrodynamics are plagued by the infrared problem, which has been a subject of study in mathematical physics for more than four decades [6,7,8,10,16,18,19,21,22,23,24,28,29,30,33,34,39,40,41,42,44,46,48]
As a step in this direction, we demonstrate in the present paper that a simple variant of this phenomenon - superselection of direction of motion - occurs in a large class of two-dimensional conformal field theories
In this work we carried out a systematic study of particle aspects of two-dimensional conformal field theories both in vacuum representations and in charged representations

Summary

Introduction

Particle aspects and superselection structure of quantum electrodynamics are plagued by the infrared problem, which has been a subject of study in mathematical physics for more than four decades [6,7,8,10,16,18,19,21,22,23,24,28,29,30,33,34,39,40,41,42,44,46,48]. Superselection of direction of motion is a milder property: It only requires that plane waves ψξ , ψξ , travelling in opposite directions, give rise to representations πξ , πξ which are not unitarily equivalent This latter interplay between the infraparticle’s kinematics and the superselection structure occurs in some two-dimensional conformal field theories, as we explain below. We state this property precisely in Definitions 2.7 and 2.12, where we restrict attention to representations π of (Murray-von Neumann) type I with atomic center.

Particle Aspects of Two-Dimensional Massless Theories

Particle Aspects of Conformal Field Theories

Conclusions and Outlook