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Chiral Anomaly in Contorted Spacetimes

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Abstract

The Dirac equation in Riemann-Cartan spacetimeswith torsion is reconsidered. As is well-known, only theaxial covector torsion A, a oneform, couples to massiveDirac fields. Using diagrammatic techniques, we show that besides the familiar Riemannianterm only the Pontrjagin type four-form dA ∧ dA doesarise additionally in the chiral anomaly, but not theNieh-Yan term d * A, as has been claimed recently.Implications for Ashtekar's canonical approach to quantumgravity are discussed.

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Authors
  1. Eckehard W. Mielke
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  2. Dirk Kreimer
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Mielke, E.W., Kreimer, D. Chiral Anomaly in Contorted Spacetimes. General Relativity and Gravitation 31, 701–712 (1999). https://doi.org/10.1023/A:1026653314045

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