Translation invariant theory of polaron (bipolaron) and the problem of quantizing near the classical solution

A physical interpretation of translation-invariant polarons and bipolarons is presented, some results of their existence are discussed. Consideration is given to the problem of quantization in the vicinity of the classical solution in the quantum field theory. The lowest variational estimate is obtained for the bipolaron energy E(η) with E(0) = -0.440636α², where α is a constant of electron-phonon coupling, η is a parameter of ion binding.