Feynman's variational principle for a polaron in a magnetic field

The validity of the generalization of Feynman's variational inequality in polaron theory to the case of an arbitrary nonvanishing constant magnetic field is investigated. It is shown that when an anisotropic trial quadratic action is used this generalization is not valid. For the linear polaron model in the case of isotropic trial quadratic action the validity of the Feyuman variational inequality is proved for all temperatures, coupling constants, and magnetic fields.