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In this article is proved the existence and uniqueness of a minimizer of theenergy for the non-relativistic one electron Pauli-Fierz model, within theclass of pure quasifree states. The minimum of the energy on pure quasifreestates coincides with the minimum of the energy on quasifree states. Infraredand ultraviolet cutoffs are assumed, along with sufficiently small couplingconstant and momentum of the dressed electron. A perturbative expression of theminimum of the energy on quasifree states for a small momentum of the dressedelectron and small coupling constant is then given. We also express theLagrange equation for the minimizer, in terms of the generalized one particledensity matrix of the pure quasifree state.

Minimization of the Energy of the Non-Relativistic One-Electron Pauli-Fierz Model over Quasifree States