The Stark problem as a concave toric domain

TL;DR

This paper demonstrates that the bounded energy regions of the planar Stark problem, after Levi-Civita regularization, can be viewed as boundaries of concave toric domains, linking a classical physics problem to symplectic geometry.

Contribution

It establishes a novel geometric interpretation of the planar Stark problem's energy hypersurfaces as boundaries of concave toric domains after regularization.

Findings

Bounded energy hypersurfaces are boundaries of concave toric domains.

The interpretation applies to energies below a critical value.

Provides a new geometric perspective on the Stark problem.

Abstract

The Stark problem is a completely integrable system which describes the motion of an electron in a constant electric field and subject to the attraction of a proton. In this paper we show that in the planar case after Levi-Civita regularization the bounded component of the energy hypersurfaces of the Stark problem for energies below the critical value can be interpreted as boundaries of concave toric domains.