Spinorial Regularization

Abstract

The results of the previous chapter do not depend on the physical dimensions of the Kepler Problem. In this chapter we will reformulate the regularization construction, but with the group SO (2, n + 1) replaced by its double covering, the so-called Spin(2, n + 1) group’⁾.

Nothing essentially new is obtained in this way and so one might ask why we discuss spinorial regularization at all. The point is that the well knownLevi-CivitaandKustaanheimo-Stie feltransformations (discoveredbeforethe Souriau-Moser regularization) are examples of the spinorial regularization (for n = 2, 3 respectively), as has been clarified by Kummer (1982).

In this chapter we will first deal with the physical case n = 3, where Spin(2, 4) = SU(2, 2) and the spinors are calledtwistors.Afterwards we generalize to arbitrary n, as in Cordani & Reina (1987) and Cordani (1989b).