  In this work we apply the Lie group representation method introduced in the
real time formalism for finite-temperature quantum-field theory, thermofield
dynamics, to derive a spinorial density matrix equation. Symmetry properties of
such equation are analysed, and as a basic result it is shown that one solution
is the generalised density matrix operator proposed by Heinz, to deal with
gauge covariant kinetic equations. In the same context, preliminary aspects of
a Lagrangian formalism to derive kinetic equations, as well as quantum density
matrix equations in curved space-time, are discussed.
