Summary
Recently improved techniques for constructing standard wave equations are demonstrated by finding all the equations in the family of those with physical spin 3/2, for which 3/2 is not also an auxiliary spin. The structure of the equations obtained is analysed with respect to the irreducible representations of the Lorentz group which they involve. The equations are also rewritten in terms of a vector-spinor field and a sequence of ordinary Dirac spinors. They are then all seen to be remarkably simple.
Riassunto
Si dimostrano tecniche recentemente migliorate per costruire equazioni d’onda standard trovando tutte le equazioni nella famiglia di quelle con spin fisico 3/2, per le quali 3/2 non è anche uno spin ausiliario. Si analizza la struttura delle equazioni ottenute rispetto alle rappresentazioni irriducibili del gruppo di Lorentz che queste implicano. Le equazioni sono anche riscritte in termini di un campo vettoriale-spinoriale e una sequenza di spinori ordinari di Dirac. Si osserva quindi che queste sono tutte notevolmente semplici.
Резюме
Недавно улучшенная техника конструирования стандартных волновых уравнений применяется для получения всех уравнений с физическим спином 3/2, для которых спин 3/2 не является вспомогательным спином. Анализируется структура полученных уравнений относительно неприводимых представлений группы Лоренца. Уравнения переписываются в терминах векторно-спинорного поля и последовательности обычных спиноров Дирака. Уравнения имеют простой вид.
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Labonté, G. On the structure of all the equations for spin 3/2 without auxiliary spin 3/2; their vector-spinor form. Nuov Cim A 80, 429–440 (1984). https://doi.org/10.1007/BF02773504
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DOI: https://doi.org/10.1007/BF02773504