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Spin and the structure of space-time

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Spin and the structure of space-time ANNALES DE L’I. H. P., SECTION A FRIEDRICH W. HEHL PAUL VON DER HEYDE Spin and the structure of space-time Annales de l’I. H. P., section A, tome 19, no 2 (1973), p. 179-196. <> © Gauthier-Villars, 1973, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A », implique l’accord avec les conditions générales d’utilisation (http://www. Toute utilisation commerciale ou impression systé- matique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques 179 Spin and the Structure of Space-Time (*) Friedrich W. HEHL Paul von der HEYDE Institute for Theoretical Physics of the Technische Universitat Clausthal, D-3392 Clausthal-Zellerfeld, West Germany " Newton successfully wrote apple = moon, but you cannot write apple=neutron. " J. L. SYNGE " ... la torsion de l’Univers continue a etre nulle dans le vide. " E. CARTAN Ann. Inst. Henri Poincaré, Vol. XIX, no 2, 1973, Section A : Physique théorique. ABSTRACT. - The gravitational field in General Relativity (GR) is coupled to the energy-momentum tensor of matter, i. e. it is the dynamical manifestation of energy-momentum. In Section 1 we try to collect all arguments which show that it is very plausible to look also for a dyna- mical manifestation of spin-angular momentum of matter. In Section 2 it turns out that this program can be fulfilled by genera- lizing Riemannian geometry of space-time to a Riemann-Cartan geometry. The affine connection is now asymmetric and chosen in such a way that the covariant derivative of the metric still vanishes. The newly intro- duced contortion tensor or, equivalently, Cartan’s torsion tensor describe independent rotational degrees of freedom of t

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