Summary
At the beginning (Sect. 2) we consider such field theories, which are characterized by operators defined on spacelike surfaces. In this connection Haag’s theorem is discussed. Then the properties of the field operator algebra are investigated (Sect. 3). It follows that the algebraB, defined in Sect. 3·5, is already cyclic. Furthermore, the algebraB, essentially arrived at by adjoining toB the projection operator onto the vacuum state, is irreducible.
Riassunto
Al principio (Sez. 2) consideriamo quelle teorie di campo che sono caratterizzate da operatori definiti in superfici spazio-simili. In relazione a questo si discute il teorema di Haag. Poi si analizzano le proprietá dell’algebra degli operatori di campo (Sez. 3). Segue ehe l’algebraB, definita nella Sez. 3·5, è già ciolica. Inoltre l’algebraB, a cui essenzialmente si perviene aggiungendo aA l’operatore di proiezione nello stato vuoto, è irriducibile.
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Reeh, H., Schlieder, S. Bemerkungen zur unitäräquivalenz von lorentzinvarianten feldern. Nuovo Cim 22, 1051–1068 (1961). https://doi.org/10.1007/BF02787889
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DOI: https://doi.org/10.1007/BF02787889