Communications in Mathematical Physics

, Volume 66, Issue 3, pp 223–265 | Cite as

The charged sectors of Quantum Electrodynamics in a framework of local observables

  • Jürg Fröhlich


The construction of charged sectors in Quantum Electrodynamics (QED) is analyzed within a framework of algebras of local observables. It is argued that charged sectors arise by composing a vacuum state with charged * morphisms of an algebra of (neutral) quasi-local observables. Charged * morphisms, in turn, are obtained as weak limits of charge transfer cocycles. These are non-local elements of the algebra of all quasi-local observables obeying “topological” commutation relations with the local charge operators. It is shown that in this framework, charged sectors are invariant under the time evolution and satisfy the relativistic spectrum condition. The total charge operator is well defined and time-independent (conserved) on all charged sectors. Under an additional hypothesis the spectrum of the total charge operator is shown to be a discrete subgroup of the real line. A generalized Haag-Ruelle scattering theory for charged infra-particles is suggested, and some comments on non-abelian gauge theories are described.


Gauge Theory Vacuum State Real Line Quantum Computing Commutation Relation 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Jürg Fröhlich
    • 1
  1. 1.Institut des Hautes Etudes ScientifiquesBures-sur-YvetteFrance

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