Quantum Metric Corrections to Liouville's Theorem and Chiral Kinetic Theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913089833664512 |
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| author | Mameda, Kazuya Yamamoto, Naoki |
| author_facet | Mameda, Kazuya Yamamoto, Naoki |
| contents | Quasiparticles may possess not only Berry curvature but also a quantum metric in momentum space. We develop a canonical formalism for such quasiparticles based on the Dirac brackets, and demonstrate that quantum metric modifies the phase-space density of states at $\mathcal{O}(\hbar^2)$, leading to corrections to Liouville's theorem, kinetic theory, and related physical quantities. In particular, we show that, in the presence of an inhomogeneous electric field, quantum metric induces corrections to the energy density and energy current. Applied to chiral fermions, this framework provides a nonlinear extension of chiral kinetic theory consistent with quantum field theory. Our work paves the way to potential applications of the quantum metric in high-energy physics and astrophysics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_15731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Metric Corrections to Liouville's Theorem and Chiral Kinetic Theory Mameda, Kazuya Yamamoto, Naoki High Energy Physics - Theory Mesoscale and Nanoscale Physics Strongly Correlated Electrons General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Quasiparticles may possess not only Berry curvature but also a quantum metric in momentum space. We develop a canonical formalism for such quasiparticles based on the Dirac brackets, and demonstrate that quantum metric modifies the phase-space density of states at $\mathcal{O}(\hbar^2)$, leading to corrections to Liouville's theorem, kinetic theory, and related physical quantities. In particular, we show that, in the presence of an inhomogeneous electric field, quantum metric induces corrections to the energy density and energy current. Applied to chiral fermions, this framework provides a nonlinear extension of chiral kinetic theory consistent with quantum field theory. Our work paves the way to potential applications of the quantum metric in high-energy physics and astrophysics. |
| title | Quantum Metric Corrections to Liouville's Theorem and Chiral Kinetic Theory |
| topic | High Energy Physics - Theory Mesoscale and Nanoscale Physics Strongly Correlated Electrons General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2509.15731 |