Chiral Anomaly in Contorted Spacetimes

Details Chiral Anomaly in Contorted Spacetimes Chiral Anomaly in Contorted Spacetimes

1997-04-18

arxiv.org/abs/gr-qc/9704051v1

Gen.Rel.Grav.31:701-712,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, REVTEX

Scientific paper

10.1023/A:1026653314045

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.

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