The origin of the Schott term in the electromagnetic self force of a classical point charge

TL;DR

This paper derives the Schott term in the electromagnetic self force of a point charge through direct integration, clarifying its origin without ad hoc additions, and compares different hypertube methods.

Contribution

It provides a direct integration approach to obtain the Schott term, resolving previous inconsistencies and clarifying its origin in the electromagnetic stress-energy-momentum tensor.

Findings

The Schott term naturally arises from direct integration.

Previous methods using Bhabha tubes failed to produce the Schott term.

The direct integration approach clarifies the origin of the Schott term.

Abstract

The Schott term is the third order term in the electromagnetic self force of a charged point particle. The self force may be obtained by integrating the electromagnetic stress-energy-momentum tensor over the side of a narrow hypertube enclosing a section of worldline. This calculation has been repeated many times using two different hypertubes known as the Dirac Tube and the Bhabha Tube, however in previous calculations using a Bhabha Tube the Schott term does not arise as a result of this integration. In order to regain the Lorentz-Abraham-Dirac equation many authors have added an ad hoc compensatory term to the non-electromagnetic contribution to the total momentum. In this article the Schott term is obtained by direct integration of the electromagnetic stress-energy-momentum tensor.