Summary
It is known that the equations for particles of spin ⩾ 3/2 become inconsistent when electromagnetic interactions are introduced by the usual rules. An analogous problem is that of the effect of the introduction of gravitational fields on the consistency of the equations. The « natural generalization » of the usual field equations for particles of spin 3/2 is here considered in detail, and it is shown that the equations are compatible if and only if the Riemann space in which the spinor field is contemplated is an Einstein space. This result is discussed.
Riassunto
È noto che le equazioni per le particelle di spin ⩾ 3/2 diventano inapplicabili quando si introducono interazioni elettromagnetiche con i metodi usuali. Un problema analogo è quello dell’effetto dell’introduzione di campi gravitazionali sull’applicabilità delle equazioni. Si considera qui dettagliatamente la « generalizzazione naturale » delle usuali equazioni del campo per particelle di spin 3/2 e si dimostra che le equazioni sono compatibili se, e solo se, lo spazio riemanniano in cui si considera il campo spinoriale è uno spazio einsteiniano. Si discute il risultato.
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Buchdahl, H.A. On the compatibility of relativistic wave equations for particles of higher spin in the presence of a gravitational field. Nuovo Cim 10, 96–103 (1958). https://doi.org/10.1007/BF02859608
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DOI: https://doi.org/10.1007/BF02859608