Non relativistic limit of the Landau-Lifshitz equation: A new equation

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• 作者：G. Ares de Parga^a ; ^{gadpau@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; S. Domí ; nguez-Herná ; ndez^b ; E. Salinas-Herná ; ndez^c
• 关键词：Radiation reaction ; Landau&ndash ; Lifshitz equation ; Ford equation ; Vlasov equation
• 刊名：Annals of Physics
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：369
• 期：Complete
• 页码：45-65
• 全文大小：645 K

文摘

It is shown that Ford equation is not adequate in general to describe the motion of a charged particle including the reaction force in the non relativistic limit. As in General Relativity where a post-Newtonian method is developed in order to describe the gravitational effects at low velocities and small energies, an extra term inherited from Special Relativity must be added to the Ford equation. This is due to that the new term is greater than the reaction force in many physical situations. The Coulombic case is analyzed showing the necessity of including the new term. Comparison with General Relativity results is analyzed. The Vlasov equation to first order in 1/c²$1/c^2$ is proposed for the constant electric and magnetic fields.