The purpose of this paper is to discuss the possibility of the elimination of the infrared divergences from the matrix elements in the massless quantum electrodynamics (QED with a massless fermion), if one takes account of the asymptotic interaction.The asymptotic interaction. The interaction Hamiltonian in terms of the creation and annihilation operators is, in the Dirac picture,The coefficients of t in the arguments of the exponential function vanish for the following processes; e=~e± + a soft or parallel hard r and a parallel e'epair ~r.So, the interaction corresponding to these processes remains at !t]-J>oo. Let us call this the asymptotic interaction H~, (t).In (1) we have omitted two terms which do not contribute at jtj-J>oo. Asymptotic space and scattering matrix elements.To define the space of the asymptotic states (the asymptotic space), let us introduce the asymptotic wave operator vVas (t) which satisfies the following asymptotic equation in the Dirac picture:In solving this equation, one must choose the boundary condition so that the wave operator TV as (t) does not contain a contribution from the integrals of H~, (t) with respect to the finite time. Now let us define the asymptotic space !Has for the massless QED as follows:(3)
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