A functional approach to the Kustaanheimo-Steifel transformation (Q1111788)

A constraint analysis of the Kepler problem with an integrated version of the Kustaanheimo-Steifel transformation gives a first-class constraint which generates a symmetry of the extended variables. The transformation is used in a functional approach to the quantum theory, showing that the transformed Lagrangian is related to that of a four-dimensional harmonic oscillator, with the functional integration over a restricted function space. Basis functions for this space are given in terms of two two- dimensional harmonic oscillators with equal angular momentum quantum numbers, and are invariant under contact transformations generated by the first-class constraint.