On Fock Transform and Moser Regularization Map

Abstract

For the Kepler problem, the Fock transform is the starting point of the quantization in the momentum representation, and its associated Moser regularization map is an imbedding of energy surfaces that yields the dynamic completion. Here, we first introduce a version of the Fock transform, with the normalization chosen so that the analytic formula for the resulting Moser regularization map exhibits a uniform dependence on the energy. Next, we provide a characterization for the Moser regularization map in terms of contact form and symmetries.