Il Nuovo Cimento (1955-1965)

, Volume 24, Issue 2, pp 214–236

On structure of the algebra of field operators

  • H. -J. Borchers
Article

Summary

Fields describable by Wightman-functions are investigated. It will be shown that for irreducible fields the lowest energy state is not degenerated. A necessary and sufficient condition for the irreducibility of the field, in terms of Wightman-functions, will be derived. For reducible fields it will be shown that the algebra of all operators commuting with the field is an abelian algebra and that its elements commute also with the representation of the inhomogeneous Lorentz-group.

Riassunto

Si studiano i campi, che possono essere descritti con funzioni di Wightmann. è stato dimostrato che nei campi irriducibili lo stato di energia minima non è degenerate In termini delle funzioni di Wightmann, si è dedotta una condizione necessaria e sufficiente per la irriducibilità del campo. Per i campi riducibili si è dimostrato che l’algebra di tutti gli operatori che commutano col campo, è un’algebra abeliana e che i suoi elementi commutano anche con la rappresentazione del gruppo di Lorentz non omogeneo.

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Copyright information

© Società Italiana di Fisica 1962

Authors and Affiliations

  • H. -J. Borchers
    • 1
  1. 1.Institute for Advanced StudyPrinceton

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