Summary
In this paper a negative answer is given to the question whether it is possible or not to describe ≪ interesting ≫ parafields of rank r > 1 in terms of destruction and creation operators obtained from the Fock unsymmetrized ones by using special sequences of central idempotents. More specifically, it is proved for such algebras that: i) no commutation relations exist which allow one to write state vectors in an ≪ almost normal ≫ form, ii) it is not possible to express the particle number operator Nk as a polynomial in certain suitable operators.
Riassunto
In questo lavoro si dà una risposta negativa al quesito se sia o no possibile descrivere paracampi ≪ interessanti ≫ di ordine r > 1 in funzione degli operatori di distruzione e creazione ottenuti da quelli non simmetrici di Fock usando sequenze speciali di idempotenti centrali. Più specincatamente, si prova che in queste algebre: 1) non esistono relazioni di commutazione che permettano di scrivere i vettori di stato in forma ≪quasi normale≫, 2) non é possibile esprimere l’operatore del numero di particelle,N k , come un polinomio di alcuni opportuni operatori.
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On leave of absence from the Junta de Energía Nuclear, Madrid.
Supported by the Comisaria de Protección Escolar.
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Galindo, A., Yndurain, P.J. On parastatistics. Nuovo Cim 30, 1040–1047 (1963). https://doi.org/10.1007/BF02828812
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DOI: https://doi.org/10.1007/BF02828812