Chiral anomaly in (1+1) dimensions revisited: complementary kinetic perspective and universality

Abstract

We reinvestigate the classic example of the chiral anomaly in (1+1) dimensional spacetime. By reviewing the derivation of charge conservation using the semiclassical Boltzmann equation, we show that chiral anomalies could emerge in (1+1) dimensions without Berry curvature corrections to the kinetic theory. The pivotal step depends only on the asymptotic behavior of the distribution function of the quasiparticle--and thus its dispersion relation--in the limit of $\mathbf{p}\to \pm \infty$ rather than the detailed functional form of the dispersion. We address two subjects motivated by this observation. First, we reformulate (1+1)-dimensional chiral anomaly using kinetic theory with the current algebra approach and the gradient expansion of the Dirac Lagrangian, adding a complementary perspective to existing approaches. Second, we demonstrate the universality of the chiral anomaly across various quasiparticle dispersions. For two-band models linear in the temporal derivative, with Fujikawa's method we show it is sufficient to have a chirality-odd strictly monotonic dispersion in order to exhibit the chiral anomaly.

6 pages, final published version

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