1997/04/18 by Eckehard W. Mielke, E. W. Mielke, Dirk Kreimer +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1023/a:1026653314045
published as Gen.Rel.Grav.31:701-712,1999 · 17 pages, REVTEX
arxiv created 1997/04/18 · openalex publication_date 1999/05/01 · arxiv updated 2011/04/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Dirac equation in Riemann-Cartan spacetimes with torsion is reconsidered. As is well-known, only the axial covector torsion A, a one-form, couples to massive Dirac fields. Using diagrammatic techniques, we show that besides the familiar Riemannian term only the Pontrjagin type four-form dA\wedge dA does arise additionally in the chiral anomaly, but not the Nieh-Yan term d ^* A, as has been claimed recently. Implications for cosmic strings in Einstein-Cartan theory as well as for Ashtekar's canonical approach to quantum gravity are discussed.