Complete determination of the thermal gauge potential from damping force

Determine completely the Abelian and non-Abelian thermal gauge potential from the temperature-dependent damping force derived within the quantum Boltzmann equation and spinor Boltzmann equation frameworks.

Background

The paper describes prior work connecting temperature-dependent damping forces, obtained from quantum Boltzmann and spinor Boltzmann equations, to Abelian U(1) and non-Abelian SU(2) or SU(3) thermal gauge potentials. However, the stated connection does not yet provide a complete determination of the gauge potential from the damping force.

The unresolved issue concerns identifying the full thermal gauge potential corresponding to a given damping force. The paper subsequently investigates an analytically constructed temperature-dependent non-Abelian gauge potential in a ferromagnetic system under the adiabatic approximation, but the broader problem of complete determination from the damping force is explicitly left open.