New light on infrared problems: sectors, statistics, symmetries and spectrum
type: Item
instance of: scholarly article
title: New light on infrared problems: sectors, statistics, symmetries and spectrum
zbMATH Open document ID: 1296.81044
author: Detlev Buchholz
author: John E. Roberts
published in: Communications in Mathematical Physics
publication date: 2014-08-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/1304.2794
review text: The aim of this article is to shed new light on an old problem in quantum field theory, occurring in particular in QED where zero-mass photons give rise to infrared singularities in the context of perturbation theory. The mathematical framework used here has become known as \textit{algebraic quantum field theory} and has been developed by Doplicher, Haag and Roberts in 1969--1997. It has has proved to be a powerful tool for explaining the superselection structure and describing sectors of physical states. Still, so far one important class of theories is not covered by this framework, i.e. when there are forces mediated by massless particles like photons in QED. Quite unexpected, there seems to be a fundamental difference between theories describing only massive particles and theories including massless particles. In particular, the notion of superselection sector provides too fine a resolution of the state space, which leads to complications, and so the aim of the present investigation is to provide a slightly changed framework using concepts closer to actual experiments taking place in future directed light cones. Any such light cone \(V\) gives rise to an algebra of local observables in \(V\). One aspect of the present approach is the endomorphic nature of time evolution. The article has eight Sections. Section 1 provides the reader with a thorough discussion of modern tools, whereas the assumptions underlying the present analysis are presented in Section 2. In Section 3, the concept of \textit{vacuum in a light cone} is introduced and its charge class is analyzed. Section 4 establishes the concept of simple charge classes and derives their group structure and statistics. In Section 5, covariant charge classes are defined admitting unitary representations of the Poincaré group, while Section 6 is devoted to a proof of the spectrum condition. In Section 7, the relation between the present approach and the standard Minkowski space interpretation is discussed. The co…
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 6324353
zbMATH Keywords: infrared singularity
zbMATH Keywords: massless particles
zbMATH Keywords: algebraic quantum field theory
zbMATH Keywords: superselection sectors
zbMATH Keywords: physical state space
zbMATH Keywords: local observable on a light cone
zbMATH Keywords: charge classes
zbMATH Keywords: statistics
zbMATH Keywords: endomorphic time evolution
reviewed by: Gert Roepstorff
MaRDI profile type: Publication
OpenAlex ID: W3102549075
arXiv ID: 1304.2794
cites work: On unitary ray representations of continuous groups
cites work: FROM QUANTUM FIELDS TO LOCAL VON NEUMANN ALGEBRAS
cites work: The physical state space of quantum electrodynamics
cites work: Q4215432
cites work: Quantum delocalization of the electric charge
cites work: Locality and the structure of particle states
cites work: Relative Haag duality for the free field in Fock representation
cites work: Homogeneity of the state space of factors of type \(III_1\)
cites work: Fields, observables and gauge transformations. II
cites work: Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics
cites work: Superselection sectors with braid group statistics and exchange algebras
cites work: BRAID STATISTICS IN LOCAL QUANTUM THEORY
cites work: Q3910965
cites work: Q4023625
cites work: Notes on algebraic invariants for non-commutative dynamical systems
cites work: Index of subfactors and statistics of quantum fields. II: Correspondences, braid group statistics and Jones polynomial
cites work: Total sets in quantum field theory
cites work: Q3769453
cites work: Q3876492
DOI: 10.1007/S00220-014-2004-2
description: scientific article