Abstract
A gauge covariant point-splitting regularisation is employed to calculate different anomalous commutators in four dimensional chiral gauge theories. For an external gauge field the fixed time anomalous commutator of the gauge group generators is seen to violate the Jacobi identity. The cohomological prediction can be confirmed provided the electric fields do not commute. Other commutators like the current-current and current-electric field are consistent with the Bjorken-Johnson-Low (BJL) derivation.
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Ghosh, S., Banerjee, R. Point-splitting analysis of commutator anomalies in non-abelian chiral gauge theories. Z. Phys. C - Particles and Fields 41, 121–127 (1988). https://doi.org/10.1007/BF01412586
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DOI: https://doi.org/10.1007/BF01412586