Self-force of uniformly accelerating charged particle in Born–Infeld electrodynamics

The self-force in the Lorentz–Abraham–Dirac equation contains a third-order time-derivative term, known as the Schott term, which results in unphysical solutions to the equation. The Schott term appears after renormalization where an infinity, which originates from the diverging self-field induced by a point charge in the Maxwell theory, is removed. The Born–Infeld model, which pertains to non-linear electrodynamics and comprises the Maxwell theory in its weak-field limit, can have a bounded value for the self-field and yield a self-force without a higher-order derivative term. Because the field solution for an arbitrary particle motion has not yet been obtained for the Born–Infeld model because of its nonlinearity, we focus on a uniformly accelerating charged particle and derive a self-force formula by using an approximate solution of the Born–Infeld field equation. It is shown that a self-force exists for a uniformly accelerating particle, whereas it diminishes in the LAD equation and does not contain a higher derivative term.