Towards a bottom-up formulation of spin kinetic theory

TL;DR

This work develops a bottom-up spin kinetic theory (SKT) for hot and/or dense plasmas by introducing a scalar phase-space distribution $f$ and an axial-vector distribution ${\bm g}$ as the dynamical variables, with dynamics governed by spin-dependent Poisson brackets and a Schwinger–Keldysh action. It provides explicit constitutive relations for vector and axial Wigner functions in terms of $(f, {\bm g})$, and derives linear-response results in both kinetic theory and field theory. A key result is the precise non-analytic matching between the two descriptions for electromagnetic and gravitational perturbations, validating the bottom-up approach as a complementary framework to traditional top-down methods. The formalism promises insights into spin dynamics in non-equilibrium media, with potential applications to hot QCD matter and polarization phenomena in heavy-ion and high-energy collisions, and suggests avenues for extending to higher gradients and Lorentz-covariant formulations.

Abstract

We develop a bottom-up formulation of spin-kinetic theory for hot and/or dense plasmas. We introduce scalar and axial-vector phase-space functions as dynamical variables that parametrize both spin-averaged and spin-dependent distribution functions. Using spin-dependent Poisson brackets, we derive the corresponding kinetic equations and construct the associated Schwinger-Keldysh action. We further demonstrate how physical observables can be expressed in terms of these dynamical variables through constitutive relations. In the linear response regime, we establish a precise matching between the kinetic-theory and field-theory descriptions of vector and axial Wigner functions under electromagnetic and gravitational perturbations. Our framework provides a complementary approach to describing the dynamics of spin effects in a medium.