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| Main Authors: | , |
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| Format: | Preprint |
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2022
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| Online Access: | https://arxiv.org/abs/2201.02844 |
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| _version_ | 1866915082089267200 |
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| author | Hsiao, Wei-Han Wang, Chiao-Hsuan |
| author_facet | Hsiao, Wei-Han Wang, Chiao-Hsuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_02844 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Chiral anomaly in (1+1) dimensions revisited: complementary kinetic perspective and universality Hsiao, Wei-Han Wang, Chiao-Hsuan High Energy Physics - Theory High Energy Physics - Phenomenology Quantum Physics 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. |
| title | Chiral anomaly in (1+1) dimensions revisited: complementary kinetic perspective and universality |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Quantum Physics |
| url | https://arxiv.org/abs/2201.02844 |