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I am trying to write the Boltzmann equation for $$H=v_{F}\vec{\sigma}\cdot(\vec{p}-e\vec{A}).$$ This is a free charged particles gas. The velocity for this hamiltonian is $$\vec{v}=v_{F} \vec{\sigma}.$$ The Lorentz force can be derived $\vec{F}=q(\vec{v}\times \vec{B})$. I am considering to start from $$\frac {df}{dt}=\frac {\partial f}{\partial t}+\vec{F}\cdot\vec{\nabla}_{p}f(\vec{p},\vec{\sigma},\epsilon).$$ I am trying to rigorously reach to boltzmann equation from this hamiltonian.

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This is discussed in detail in the paper Chiral Kinetic theory by Stephanov and Yin arXiv:1207.0747

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  • $\begingroup$ Thanks @ mike stone $\endgroup$ – Hazoor Imran Apr 10 '19 at 1:04

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