Study of a model of quantum electrodynamics

This pare studies the model of the quantum electrodynamics (QED) of a singl e nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The infrared divergence is associated with the inequivalence of th e Hilbert spaces associated with the free Hamiltonian and with the complete Hamiltonian. Infrared divergences that are visible in the perturbative des cription disappear in the space of the clothed electrons. In this model whe n the Hamiltonian is expressed in the space of the clothed electrons. In th is model when the Hamiltonian is expressed in terms of the "physical" field s that create the electron together with its cloud of soft photons, the var iational principle suggested earlier can be applied. At finite time the Hei senberg field of the model acts in the space of the perturbative electron t ogether with a finite number of perturbative photons, while the "physical" field can be chosen to act in the space of the exact ("physical") electron eigenstates together with a finite number of physical photons. The space od the physical (or clothed) electron states can be chosen to be a Fock space .