97-176 D. Noja, A. Posilicano

On the Point Limit of the Pauli-Fierz Model (282K, postscript) Apr 7, 97

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Abstract. We continue in this paper the analysis of the classical dynamics of the point limit of the Maxwell--Lorentz system in dipole approximation ( the Pauli--Fierz model ). Here, as a first step towards considering the full nonlinear system, we study the case in which a nonlinear external field of force is present. We study the flow of the regularized ( namely with an extended particle ) system, and show that it converges in the appropriate norm, as the radius of the particle tends to zero, to the flow of a closed coupled system of equations, containing the renormalized mass only, which so provides the very definition of the dynamics of the system in the point limit. The Abraham--Lorentz--Dirac equation for the particle position is deduced and turns out to be, in this description, a boundary condition on the vector potential, giving the evolution of its singularity. Moreover, the Hamiltonian structure of the limit system is displayed, and it is shown that the standard Hamiltonian of the Pauli--Fierz model converges to the Hamiltonian of the limit system here given.

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