Spinorial Matter in Affine Theory of Gravity and the Space Problem |
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Authors: | Horst–Heino V Borzeszkowski Hans–Jürgen Treder |
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Institution: | (1) Institute for Theoretical Physics, Technical University Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany;(2) Rosa–Luxemburg–Str. 17a, D-14482 Potsdam;, Germany |
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Abstract: | The purely affine theory of gravity possesses a canonical formulation. For this and other reasons, it could be a promising candidate for quantum gravity. Motivated by these perspectives, we discuss spinorial matter coupled to gravity, where the latter is described by a connection having no a priori relation to a metric. We show that one can establish a truncated spinor formalism which, for special or approximate solutions to the gravitational equations, reduces to the standard formalism. As a consequence, one arrives at "matter-induced" Riemann–Cartan spaces solving the Weyl-Cartan space problem. |
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Keywords: | Affine spaces spinorial matter Riemann– Cartan spaces |
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