Advances in Applied Clifford Algebras

, Volume 22, Issue 3, pp 873–909 | Cite as

Fiber Bundles, Connections, General Relativity, and the Einstein-Cartan Theory – Part II



The formalism of tetrads and spin connections is presented, and with it, the Einstein-Cartan (E-C) equations are derived from the usual actions. It is shown how torsion vanishes in the case of pure gravity. Then, the equations in the presence of the Dirac and the Maxwell fields are derived. A possibility of choosing a locally inertial coordinate system in the presence of a totally antisymmetric torsion is proved. We discuss a conflict between torsion and the local gauge invariance of the electromagnetic field. Finally, we study Lorentz and Poincaré gauge invariance of general relativity and the E-C theory.

Mathematics Subject Classification (2010)

53C05 83D05 20G45 


Tetrad formalism Poincaré gauge invariance torsion vs. internal symmetries 


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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Instituto de Ciencias NuclearesUniversidad Nacional Autónoma de México Circuito ExteriorMéxicoMéxico

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