PT-symmetric interpretation of the electromagnetic self-force

TL;DR

This paper demonstrates that the electromagnetic self-force problem can be addressed using PT symmetry, which, when unbroken, removes runaway modes and ghost states in the quantum theory.

Contribution

It introduces a PT-symmetric interpretation of Englert's Hamiltonian, showing how to eliminate classical and quantum instabilities by tuning interactions into an unbroken PT-symmetric phase.

Findings

PT symmetry is broken in Englert's original model.

Adjusting coupling parameters restores unbroken PT symmetry.

Unbroken PT symmetry removes runaway modes and ghost states.

Abstract

In 1980 Englert examined the classic problem of the electromagnetic self-force on an oscillating charged particle. His approach, which was based on an earlier idea of Bateman, was to introduce a charge-conjugate particle and to show that the two-particle system is Hamiltonian. Unfortunately, Englert's model did not solve the problem of runaway modes, and the corresponding quantum theory had ghost states. It is shown here that Englert's Hamiltonian is PT symmetric, and that the problems with his model arise because the PT symmetry is broken at both the classical and quantum level. However, by allowing the charged particles to interact and by adjusting the coupling parameters to put the model into an unbroken PT-symmetric region, one eliminates the classical runaway modes and obtains a corresponding quantum system that is ghost free.