A. Zee, Quantum Field Theory in a Nutshell · Problem V.7.13

Field Theory Redux

Physics — QFT

Problem

Prove that higher order corrections do not change the chiral anomaly

\partial_\mu J_5^\mu = [1/(4\pi)^2]\epsilon^{\mu\nu\lambda\sigma} \text{tr} F_{\mu\nu}F_{\lambda\sigma}

(I have rescaled

A \to (1/g)A

). [Hint: Integrate over spacetime and show that the left hand side is given by the number of right-handed fermion quanta minus the number of left-handed fermion quanta, so that both sides are given by integers.]

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