Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory

We derive the Boltzmann equation and the collision kernel for massive spin-1/2 particles, using the Wigner-function formalism and employing an expansion in powers of.. The phase space is enlarged to include a variable related to the spin degrees of freedom. This allows us to reduce the transport equations of the independent components of the Wigner function to one scalar equation. To next-to-leading order in., we find that the collision kernel contains both local and nonlocal terms. We show that off-shell contributions cancel in the Boltzmann equation. Our framework can be used to study spin-polarization phenomena induced by vorticity as recently observed in heavy-ion collisions and in condensed-matter systems.

Automated summary

In this study, the Boltzmann equation and collision kernel for massive spin-1/2 particles were derived using the Wigner-function formalism and an expansion in powers of., The phase space was enlarged to include a variable related to spin degrees of freedom, which allowed for the reduction of transport equations to a scalar equation for independent components of the Wigner function. At next-to-leading order in., it was discovered that the collision kernel contains both local and nonlocal terms, with off-shell contributions being shown to cancel in the Boltzmann equation. It was also noted that this framework can be used to study spin-polarization phenomena induced by vorticity in heavy-ion collisions and condensed-matter systems.