Journal of Statistical Physics

, Volume 26, Issue 2, pp 347–364 | Cite as

States of one-dimensional Coulomb systems as simple examples of θ vacua and confinement

  • Michael Aizenman
  • Jürg Fröhlich


The one-dimensional Coulomb system is known to have equilibrium states with nonvanishing electric field. These states are shown here to be analogous, and related, to theθ vacua which have been discussed for gauge theories in two or more space-time dimensions. The system exhibits confinement of fractional charges, which we dicuss with the purpose of offering a simple example of theθ-vacua phenomenology. Precise relations and connections between one-dimensional Coulomb gases and two-dimensional Abelian gauge theories, and quantum-mechanical matter systems, are discussed.

Key words

Coulomb systems θ vacua confinement one-dimensional model 


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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • Michael Aizenman
    • 1
  • Jürg Fröhlich
    • 2
  1. 1.Department of PhysicsPrinceton UniversityPrincetonUSA
  2. 2.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance

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