Summary
We study the covariance properties of Murai’s, Dirac-Murai’s and Todorov’s spinor wave equations in the wholeM 2N,2 space with respect to SO{2N,2} group rotations. These rotations are in two-to-one correspondence with the conformai transformations in theM 2N,2-1,1 space, obtained by imposing the η2 = 0 cone condition on theM 2N,2co-ordinates {ηA} and passing to homogeneous co-ordinates. We investigate if and how the above-mentioned equations keep their covariance with respect toSO 2N,2group rotations,i.e. with respect to conformai transformations in the M2N-1,1 space, as soon as the η2 = 0 constraint is imposed.
Riassunto
Si studiano le proprietà di covarianza delle equazioni d’onda spinoriali di Murai, di Dirac-Murai e di TodoTov in tutto lo spazioM 2N,2rispetto alle rotazioni del gruppoSO 2N,2. Queste rotazioni sono in corrispondenza due a uno con le trasformazioni conformi nello spazio M2N-1,1, ottenuto imponendo la condizione di cono η2 = 0 sulle coordinate {η A} diM 2N,2e passando a coordinate omogenee. Si investiga se ed in qual modo le summenzionate equazioni mantengano la loro covarianza rispetto alle rotazioni del gruppoSO 2N,2, cioè rispetto alle trasformazioni conformi nello spazio M{2N-1,1}, allorché è imposto il vincolo η2 = 0.
Резюме
Мы исследуем свойства ковариантности волновых спинорных уравнений Мурея, Дирака-Мурея и Тодорова во всем пространстве M2N,2 относительно вращений группы SO2N,2-Эти вращения соответствуют два к одному конформным преобразованиям в пространстве M2N-1,1, полученном при наложении условия конуса η2 = 0 на координаты {ηA} пространства М2N,2 и переходя к однородным координатам. Мы исследуем, являются ли и каким образом вышеуказанные уравнения сохраняют ковариантность относительно вращений группы SO2N,2, т.е. относительно конформных преобразований в пространстве М2N-1,1, как только налагается ограничение η2 = 0.
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Furlan, P. AreSO 2N,2 -covariant spinor wave equations also « conformal »covariant?. Nuov Cim A 71, 43–71 (1982). https://doi.org/10.1007/BF02766692
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DOI: https://doi.org/10.1007/BF02766692