General Relativity and Gravitation

, Volume 10, Issue 4, pp 321–334 | Cite as

Point splitting in a curved space-time background: I. Gravitational contribution to the axial anomaly

  • P. A. J. Liggatt
  • A. J. Macfarlane
Research Articles


A prescription is given for point splitting in a curved space-time background which is a natural generalization of that familiar in quantum electrodynamics and Yang-Mills theory. It is applied (to establish its validity) to the verification of the gravitational anomaly in the divergence of a fermion axial current. Notable features of the prescription are that it defines a point-split current that can be differentiated straightforwardly, and that it involves a natural way of averaging (four-dimensionally) over the directions of point splitting. The method can extend directly from the spin-1/2 fermion case treated to other cases, e.g., to spin-3/2 Rarita-Schwinger fermions.


Differential Geometry Notable Feature Natural Generalization Axial Current Point Splitting 
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Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • P. A. J. Liggatt
    • 1
  • A. J. Macfarlane
    • 1
  1. 1.D.A.M.T.P.Cambridge UniversityUK

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