Radiation-reaction on the straight-line motion of a point charge accelerated by a constant applied electric field in an electromagnetic Bopp-Landé-Thomas-Podolsky vacuum

Mcguigan, R.J. and Kiessling, M.K.-H. (2026) Radiation-reaction on the straight-line motion of a point charge accelerated by a constant applied electric field in an electromagnetic Bopp-Landé-Thomas-Podolsky vacuum. International Journal of Modern Physics A, 41 (9): 2650044. ISSN 0217-751X

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Abstract

The radiation-reaction problem of standard Lorentz electrodynamics with point charges is pathological, standing in contrast to Bopp–Landé–Thomas–Podolsky (BLTP) electrodynamics, where it is in fact well defined and calculable, as reported in Ref. 20 . To demonstrate the viability of BLTP electrodynamics, we consider the BLTP analogue of the radiation reaction of a classical point charge accelerated from rest by a static homogeneous capacitor plate field, and calculate it up to [Formula: see text] in a formal expansion about [Formula: see text] in powers of ϰ, Bopp’s reciprocal length, a new electrodynamics parameter introduced by BLTP theory. In Ref. 11 , the radiation-reaction corrections to test-particle motion were explicitly computed to [Formula: see text], the first nonvanishing order. In this paper, a crucial question regarding this “small-ϰ” expansion, raised in Ref. 11 , is answered as follows: The motions computed with terms [Formula: see text] included are mathematically accurate approximations to physically reasonable solutions of the actual BLTP initial value problem for short times t, viz. when [Formula: see text], where c is the speed of light in vacuo, but their unphysical behavior over much longer times does not accurately approximate the actual BLTP solutions even when the dimensionless parameter [Formula: see text], where e is the elementary charge and [Formula: see text] the bare rest mass of the electron. This has the important implication that BLTP electrodynamics remains a viable contender for an accurate classical electrodynamics with point charges that does not suffer from the infinite self-interaction problems of textbook Lorentz electrodynamics with point charges.