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General relativity with spin and torsion: Foundations and prospects. (English) Zbl 1371.83017
Summary: A generalization of Einstein’s gravitational theory is discussed in which the spin of matter as well as its mass plays a dynamical role. The spin of matter couples to a non-Riemannian structure in space-time, Cartan’s torsion tensor. The theory which emerges from taking this coupling into account, the U4 theory of gravitation, predicts, in addition to the usual infinite-range gravitational interaction medicated by the metric field, a new, very weak, spin contact interaction of gravitational origin. We summarize here all the available theoretical evidence that argues for admitting spin and torsion into a relativistic gravitational theory. Not least among this evidence is the demonstration that the U4 theory arises as a local gauge theory for the PoincarĂ© group in space-time. The deviations of the U4 theory from standard general relativity are estimated, and the prospects for further theoretical development are assessed.

MSC:
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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