The Dirac equation in curved spacetimes using coordinate-free notation

Abstract

The Dirac equation in curved spacetimes is formulated using coordinate-free notation. A Lagrangean density which corresponds to the subject equation is presented. The subject equation is invariant under a local rotation of the coframe. The current is independent of the local orientation of the coframe and it is conserved. The subject equation has an equivalent formulation which uses the Christoffel gamma. The stress-energy tensor is calculated.

29 pages. V2: corrected a result

References in corpus (5)

• Metric-affine approach to teleparallel gravity
• Lessons of spin and torsion: Reply to ``Consistent coupling to Dirac fields in teleparallelism"
• Symmetries and supersymmetries of the Dirac operators in curved spacetimes
• A gauge model with spinor group for a description of local interaction of a fermion with electromagnetic and gravitational fields
• A coordinateless form of the Dirac equation