Abstract
We present a general theory of covariant derivative operators (linear connections) on a Minkowski manifold (represented as an affine space (M, M*) using the powerful multiform calculus. When a gauge metric extensor G (generated by a gauge distortion extensor h) is introduced in the Minkowski manifold, we get a theory that permits the introduction of general Riemann-Cartan-Weyl geometries. The concept of gauge covariant derivatives is introduced as the key notion necessary to generate linear connections that are compatible with G, thus, permitting the construction of Riemann-Cartan geometries. Many results of genuine mathematical interest are obtained. Moreover, such results are fundamental for building a consistent formulation of a theory of the gravitational field in flat spacetime. Some important examples of applications of our theory are worked in details.
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Fernández, V.V., Moya, A.M., Rodrigues, W.A. (2000). Covariant Derivatives on Minkowski Manifolds. In: Abłamowicz, R., Fauser, B. (eds) Clifford Algebras and their Applications in Mathematical Physics. Progress in Physics, vol 18. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1368-0_19
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DOI: https://doi.org/10.1007/978-1-4612-1368-0_19
Publisher Name: Birkhäuser, Boston, MA
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