Apparently, no rigorous results exist for the dynamics of a classical point particle interacting with the electromagnetic field, as described by the standard Maxwell-Lorentz equations. Some results are given here for the corresponding linearized system (dipole approximation) in the presence of a mechanical linear restoring force. We consider a regularization of the system (Pauli-Fierz model), and explicitly solve the Cauchy problem in terms of normal modes. Then we study the limit of the particle's motion as the regularization is removed. We prove that the particle's motion corresponding to smooth initial data for the field has a well-defined limit if mass is renormalized, while the motion is trivial (i.e. the particle does not move at all) if mass is not renormalized. Moreover, the limit particle's motion corresponding to an interesting class of initial data satisfies exactly the Abraham-Lorentz-Dirac equation. Finally, for generic initial data the limit motion is runaway

Bambusi, D., Noja, D. (1996). On classical electrodynamics of point particles and mass renormalization: some preliminary results. LETTERS IN MATHEMATICAL PHYSICS, 37(4), 449-460 [10.1007/BF00312675].

On classical electrodynamics of point particles and mass renormalization: some preliminary results

NOJA, DIEGO DAVIDE
1996

Abstract

Apparently, no rigorous results exist for the dynamics of a classical point particle interacting with the electromagnetic field, as described by the standard Maxwell-Lorentz equations. Some results are given here for the corresponding linearized system (dipole approximation) in the presence of a mechanical linear restoring force. We consider a regularization of the system (Pauli-Fierz model), and explicitly solve the Cauchy problem in terms of normal modes. Then we study the limit of the particle's motion as the regularization is removed. We prove that the particle's motion corresponding to smooth initial data for the field has a well-defined limit if mass is renormalized, while the motion is trivial (i.e. the particle does not move at all) if mass is not renormalized. Moreover, the limit particle's motion corresponding to an interesting class of initial data satisfies exactly the Abraham-Lorentz-Dirac equation. Finally, for generic initial data the limit motion is runaway
Articolo in rivista - Articolo scientifico
Classical electrodynamics; Dipole approximation; Mass renormalization; Point particles
English
1996
37
4
449
460
reserved
Bambusi, D., Noja, D. (1996). On classical electrodynamics of point particles and mass renormalization: some preliminary results. LETTERS IN MATHEMATICAL PHYSICS, 37(4), 449-460 [10.1007/BF00312675].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/17793
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