Classification of the Orthogonal Separable Webs for the Hamilton-Jacobi and Klein-Gordon Equations on 3-Dimensional Minkowski Space

TL;DR

This paper classifies all orthogonal separable coordinate systems in 3D Minkowski space for solving the Hamilton-Jacobi and Klein-Gordon equations, introducing a more efficient theoretical approach.

Contribution

It provides an invariant classification of 45 orthogonal webs and 88 coordinate charts using a new theory based on concircular tensors and warped products.

Findings

45 orthogonal separable webs classified

88 inequivalent coordinate charts identified

New webs not previously documented

Abstract

We review a new theory of orthogonal separation of variables on pseudo-Riemannian spaces of constant zero curvature via concircular tensors and warped products. We then apply this theory to three-dimensional Minkowski space, obtaining an invariant classification of the forty-five orthogonal separable webs modulo the action of the isometry group. The eighty-eight inequivalent coordinate charts adapted to the webs are also determined and listed. We find a number of separable webs which do not appear in previous works in the literature. Further, the method used seems to be more efficient and concise than those employed in earlier works.