Solution of Bloch equation in the Weyl representation

The Weyl symbol of the operator exponential $\exp\{-\beta[(2\mu)^{-1}\hat{p^2}+V\hat{(q)}]\}$ is regarded as a solution of the Bloch equation in the phase space. The unperturbed equation is separated in accordance with the $\hbar$ expansion of the product of Weyl symbols. The exact solution and Green's function of the unperturbed Bloch equation are found in analytic form. An iterative procedure for constructing the perturbation-theory series is proposed.