Summary
This is the third paper in a series of three papers which considers the physical properties of torsions in Riemann-Cartan space-timesU 4. Paper III briefly considers some of the simpler generalizations of the ECSK theory together with their covering theories, and a simple classification scheme for torsions is introduced that depends in part on the Weyl conformal curvature tensor. Moreover, further consideration is given to the possible physical role of the third-order «spin» tensor of Lanczos and to observations that could be made with spinning and nonspinning test particles. In particular, we consider the possible importance of the LanczosV 4 variational identity with Riemannian constraints in connection with speculations concerning the question of their microphysical significance.
Riassunto
Questo è il terzo di una serie di tre lavori che riguardano le proprietà fisiche delle torsioni negli spazi-tempoU 4 di Riemann-Cartan. Il lavoro III considera brevemente alcune delle più semplici generalizzazioni della teoria di ECSK, insieme con le loro teorie di copertura, e si introduce un semplice schema di classificazione per torsioni, che dipende in parte dal tensore di curvatura conformale di Weyl. Inoltre, si dà ulteriore considerazione al possibile ruolo fisico del tensore di «spin» di terz'ordine di Lanczos e alle considerazioni che si potrebbero fare con particelle test spinning e non spinning. In particolare, si considera la possibile importanza dell'identità variazionale del LanczosV 4 con vincoli riemanniani in rapporto alle speculazioni che riguardano la questione del loro significato microfisico.
Резюме
Эта работа представляет третью статью из серии, посвященной исследованию физических свойств кручений в пространстве-времениU 4 Римана-Картана. В этой статье вкратце рассматриваются некоторые простые обобщения теории Эйнштейна-Картана-Шиама-Киббла. Вводится простая схема классификации для кручений, которая частично зависит от конформного техзора кривизны Вейля. Также обсуждаются возможная физическая роль «спинового» тензора третьего порядка Ланцоша и измерения, которые могли бы быть проведены с «вращающимися» и «невращающимися» пробными частицами. В частности, мы отмечаем важностьV 4 вариационного тождества Ланцоша с ограничениями Римана в связи с рассуждениями, касающимися вопроса о их микрофизической значимости.
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References
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Davis, W.R., Atkins, W.K. & Baker, W.M. On the properties of torsions in Riemann-Cartan space-times. III: Classification of torsion and general discussion. Nuov Cim B 44, 23–38 (1978). https://doi.org/10.1007/BF02730330
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DOI: https://doi.org/10.1007/BF02730330