Understand
In view of the recent applications of chiral anomaly to various fields beyond particle physics, we discuss some basic aspects of chiral anomaly which may help deepen our understanding of chiral anomaly in particle physics also.
- It is first shown that Berry's phase (and its generalization) for the Weyl model $H =v_{F} \vec{\sigma}\cdot \vec{p}(t)$ assumes a monopole form at the exact adiabatic limit but deviates from it off the adiabatic limit and vanishes in the high frequency limit of the Fourier transform of $\vec{p}(t)$ for bounded $|\vec{p}(t)|$.
- An effective action, which is consistent with the non-adiabatic limit of Berry's phase, combined with the Bjorken-Johnson-Low prescription gives normal equal-time space-time commutators and no chiral anomaly.
- In contrast, an effective action with a monopole at the origin of the momentum space, which describes Berry's phase in the precise adiabatic limit but fails off the adiabatic limit, gives anomalous space-time commutators and a covariant anomaly to the gauge current.