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arXiv · 1909.01791

Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation

Friedrich W. Hehl·Yuri N. Obukhov
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Abstract

According to Yang \& Mills (1954), a {\it conserved} current and a related rigid (`global') symmetry lie at the foundations of gauge theory. When the rigid symmetry is extended to a {\it local} one, a so-called gauge symmetry, a new interaction emerges as gauge potential $A$; its field strength is $F\sim {\rm curl} A$. In gravity, the conservation of the energy-momentum current of matter and the rigid translation symmetry in the Minkowski space of special relativity lie at the foundations of a gravitational gauge theory. If the translation invariance is made local, a gravitational potential $\vartheta$ arises together with its field strength $T\sim {\rm curl}\,\vartheta$. Thereby the Minkowski space deforms into a Weitzenböck space with nonvanishing torsion $T$ but vanishing curvature. The corresponding theory is reviewed and its equivalence to general relativity pointed out. Since translations form a subgroup of the Poincaré group, the group of motion of special relativity, one ought to straightforwardly extend the gauging of the translations to the gauging of full Poincaré group thereby also including the conservation law of the {\it angular momentum} current. The emerging Poincaré gauge (theory of) gravity, starting from the viable Einstein-Cartan theory of 1961, will be shortly reviewed and its prospects for further developments assessed.

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Friedrich W. Hehl, Yuri N. Obukhov. 2020-11-21. Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation. https://doi.org/10.1007/978-3-030-51197-5_10

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