Towards a bottom-up formulation of spin kinetic theory

TL;DR

This paper introduces a bottom-up spin-kinetic theory for plasmas, using phase-space functions and Poisson brackets to connect kinetic and field-theoretic descriptions of spin dynamics.

Contribution

It develops a novel bottom-up formulation of spin-kinetic theory, incorporating scalar and axial-vector phase-space functions and establishing a link between kinetic and field theories.

Findings

Derived kinetic equations using spin-dependent Poisson brackets.

Constructed the Schwinger-Keldysh action for spin dynamics.

Established a matching between kinetic and field-theoretic descriptions in linear response.

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.