Gauge invariance and weak forces in an isotropic medium

We demonstrate that the neutrino kinetic equation derived by the standard Bogolyubov method is formally gauge non-invariant and give a recipe how to recast it to the gauge invariant form recovering the standard Lorentz form weak force term which apparently conserves the lepton current. The analogy with the QED plasma case is traced which in asymptotic regions implies substitution of electric charge $e$ by the induced electric charge $e_{\nu}^{ind}$ of neutrino within the phase factor connecting neutrino gauge invariant and non-invariant distribution functions.