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arXiv · 2202.10160

Lorentz-covariant kinetic theory for massive spin-1/2 particles

Xin-Li Sheng·Qun Wang·Dirk H. Rischke
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Abstract

We construct a matrix-valued spin-dependent distribution function (MVSD) for massive spin-1/2 fermions and study its properties under Lorentz transformations. Such transformations result in a Wigner rotation in spin space and in a nontrivial matrix-valued shift in space-time, which corresponds to the side jump in the massless case. We express the vector and axial-vector components of the Wigner function in terms of the MVSD and show that they transform in a Lorentz-covariant manner. We then construct a manifestly Lorentz-covariant Boltzmann equation which contains a nonlocal collision term encoding spin-orbit coupling. Finally, we obtain the spin-dependent distribution function in local equilibrium by demanding detailed balance.

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Xin-Li Sheng, Qun Wang, Dirk H. Rischke. 2022-02-21. Lorentz-covariant kinetic theory for massive spin-1/2 particles. https://doi.org/10.1103/physrevd.106.l111901

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