Chiral Anomaly in (1 + 1) Dimensions Revisited: Complementary Kinetic Perspective and Universality
Journal
Journal of the Physical Society of Japan
Journal Volume
93
Journal Issue
11
ISSN
0031-9015
1347-4073
Date Issued
2024-11-15
Author(s)
Hsiao, Wei-Han
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 p → ±∞ 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.
Publisher
Physical Society of Japan
Type
journal article