Einstein and the old quantum theory

TL;DR

This paper discusses Einstein's critique of Sommerfeld's quantum conditions, proposing a canonically invariant rule and exploring invariance in configuration space related to quantum theory and classical mechanics.

Contribution

It introduces a canonically invariant rule for quantum conditions and analyzes invariance properties in configuration space within the old quantum theory.

Findings

Einstein's proposed invariance addresses coordinate dependence issues.

Configuration space invariance involves loop deformations and point transformations.

Features of the Liouville-Arnol'd theorem are relevant to the invariance discussion.

Abstract

Objecting that Sommerfeld's quantum conditions refer to particular coordinates, Einstein proposes a canonically invariant rule. But even if the invariance is canonical, Einstein may have in mind a double \emph{configuration} space invariance: with respect to loop deformations, and to \emph{point} transformation -- all on a torus where features of the Liouville-Arnol'd theorem already appear.