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Communications in Mathematical Physics

, Volume 330, Issue 3, pp 935–972 | Cite as

New Light on Infrared Problems: Sectors, Statistics, Symmetries and Spectrum

  • Detlev BuchholzEmail author
  • John E. Roberts
Article

Abstract

A new approach to the analysis of the physical state space of a theory is presented within the general setting of local quantum physics. It also covers theories with long range forces, such as quantum electrodynamics. Making use of the notion of charge class, an extension of the concept of superselection sector, infrared problems are avoided by restricting the states to observables localized in a light cone. The charge structure of a theory can be explored in a systematic manner. The present analysis focuses on simple charges, thus including the electric charge. It is shown that any such charge has a conjugate charge. There is a meaningful concept of statistics: the corresponding charge classes are either of Bose or of Fermi type. The family of simple charge classes is in one-to-one correspondence with the irreducible unitary representations of a compact Abelian group. Moreover, there is a meaningful definition of covariant charge classes. Any such class determines a continuous unitary representation of the Poincaré group or its covering group satisfying the relativistic spectrum condition. The resulting particle aspects are also briefly discussed.

Keywords

Massless Particle Double Cone Superselection Sector Hyperbolic Cone Infrared Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institut für Theoretische Physik, Courant Centre “Higher Order Structures in Mathematics”Universität GöttingenGöttingenGermany
  2. 2.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomeItaly

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