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  1. A Review About Invariance Induced Gravity: Gravity and Spin from Local Conformal-Affine Symmetry. [REVIEW]S. Capozziello & M. De Laurentis - 2010 - Foundations of Physics 40 (7):867-899.
    In this review paper, we discuss how gravity and spin can be obtained as the realization of the local Conformal-Affine group of symmetry transformations. In particular, we show how gravitation is a gauge theory which can be obtained starting from some local invariance as the Poincaré local symmetry. We review previous results where the inhomogeneous connection coefficients, transforming under the Lorentz group, give rise to gravitational gauge potentials which can be used to define covariant derivatives accommodating minimal couplings of matter, (...)
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  • The structure of singularities in space-times with torsion.L. C. Garcia de Andrade - 1990 - Foundations of Physics 20 (4):403-416.
    An analysis of the extension of the Hawking-Penrose singularity theorem to Riemann-Cartan U4 space-times with torsion and spin density is undertaken. The minimal coupling principle in U4 is used to formulate a new expression for the convergence condition autoparallels in Einstein-Cartan theory. The Gödel model with torsion is given as an example.
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  • An Assessment of Evans' Unified Field Theory I.Friedrich W. Hehl - 2007 - Foundations of Physics 38 (1):7-37.
    Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe ϑ α and a (metric compatible) Lorentz connection Γ α β . These two potentials yield the field strengths torsion T α and curvature R α β . Evans tried to infuse electromagnetic properties into this geometrical framework by putting the coframe ϑ α to be proportional to four extended electromagnetic (...)
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  • Noncommutative Momentum and Torsional Regularization.Nikodem Popławski - 2020 - Foundations of Physics 50 (9):900-923.
    We show that in the presence of the torsion tensor \, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by \. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, \, where U is a constant on the order of the squared inverse of the Planck mass. We propose that this relation replaces the integration (...)
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  • An Assessment of Evans' Unified Field Theory II.Friedrich W. Hehl & Yuri N. Obukhov - 2007 - Foundations of Physics 38 (1):38-46.
    Evans attempted to develop a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for a theory that implements some of the ideas that have been (imprecisely) indicated by Evans and show that it yields two field equations. The second field equation is algebraic in the torsion and we can resolve (...)
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