Dirac equation in curved spacetimes using coordinate-free notation

Details Dirac equation in curved spacetimes using coordinate-free notation Dirac equation in curved spacetimes using coordinate-free notation

2010-06-07

arxiv.org/abs/1006.1344v1

Physics

Mathematical Physics

27 pages

Scientific paper

The Dirac equation in curved spacetimes is formulated using coordinate-free notation. A Lagrangean density which corresponds to the subject equation is presented. It is shown that the subject equation is invariant under a local rotation of the coframe. It is shown that the current is independent of the local orientation of the coframe and that it is conserved. It is shown that the subject equation has an equivalent formulation which uses the Christoffel gamma. A calculation of the stress-energy tensor in teleparallel gravity replicates the result that a version of the teleparallel equivalent of general relativity is inconsistent in the presence of a Dirac field.

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