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Letters in Mathematical Physics

, Volume 106, Issue 2, pp 269–285 | Cite as

The Universal C*-Algebra of the Electromagnetic Field

  • Detlev Buchholz
  • Fabio Ciolli
  • Giuseppe Ruzzi
  • Ezio Vasselli
Article

Abstract

A universal C*-algebra of the electromagnetic field is constructed. It is represented in any quantum field theory which incorporates electromagnetism and expresses basic features of the field such as Maxwell’s equations, Poincaré covariance and Einstein causality. Moreover, topological properties of the field resulting from Maxwell’s equations are encoded in the algebra, leading to commutation relations with values in its center. The representation theory of the algebra is discussed with focus on vacuum representations, fixing the dynamics of the field.

Keywords

electromagnetic field de Rham theory local algebras dynamical ideals Haag–Kastler axioms 

Mathematics Subject Classification

81V10 81T05 14F40 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Detlev Buchholz
    • 1
  • Fabio Ciolli
    • 2
  • Giuseppe Ruzzi
    • 2
  • Ezio Vasselli
    • 2
  1. 1.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany
  2. 2.Dipartimento di MatematicaUniversitá di Roma “Tor Vergata”RomeItaly

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