Summary
We solve the problem of finding all the possible standard relativistic equations for higher spins (i.e. s>1) with Harish-Chandra degree four. It is found that there can be only two such equations. One is the well-known Fierz-Pauli (or Rarita-Schwinger) spin-3/2 equation. The other one is a 40-component spin-3/2 equation characterized by one arbitrary nonzero real parameterk and one sign ɛ. All the pertinent matrices,i.e. Γ µ ,J i ,N i , η, for the latter are found explicitly hereafter.
Riassunto
Si risolve il problema di trovare tutte le possibili equazioni standard relativistiche per spin piú grandi (i.e. s>1) con grado quattro di Harish-Chandra. Si trova che ci possono essere solo due equazioni di questo tipo. Una è la nota equazione con spin 3/2 di Fierz-Pauli (o Rarita-Schwinger). L'altra è un'equazione a 40 componenti con spin 3/2 caratterizzata da un parametro arbitrario non nullok e un segno ɛ. Si trovano esplicitamente tutte le matrici pertinenti, cioèΓ µ ,J i ,N i , η, per quest'ultima.
Резюме
Мы решаем проблему получения всех возможных стандартных релятивистских уравнений для высших спинов (s>1) в случае четырех степеней Хариша-Чандра. Показывается, что можно получить только два таких уравнения. Одно из них—хорошо известное уравнение Фирца-Паули (или Рарита-Швингера) для спина 3/2. Другое уравнение есть 40-компонентное уравнение для спина 3/2, которое характеризуется одним произвольным ненулевым вещественным параметромk и знаком ɛ. Явным образом определяются все соответствующие матрицы для последнего уравнения, т.е.Γ µ ,J i ,N i , η.
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Footnotes
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Labonté, G. The finding of all higher-spin equations with Harish-Chandra degree four. Nuov Cim A 80, 77–88 (1984). https://doi.org/10.1007/BF02786216
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DOI: https://doi.org/10.1007/BF02786216