Quantum Dynamics from Pure Spinor Geometry
P.A.M. Dirac wrote in 1937 that from the available data in cosmology and atomic physics, he could induce the existence of "a deep connection in Nature between cosmology and atomic theory". In this paper we try to show how this connection indeed may be found in the elementary part of pure spinor geometry (two component spinors) which naturally contains the two systems of equations of motion for massless systems: the Weyl's and the consequent Maxwell's ones. Then the implied conformally compactified space-time (Robertson-Walker Universe) and the dual momentum space offer the possibility of computing some of the data (like the elementary time h/Mc2) on which Dirac based his conjecture.
For higher component pure spinors the associated Clifford algebras geometry notoriously explain several properties of elementary particles. But specially suggest that quantum dynamics may be formulated and rationally understood, rather than in space-time, in momentum space where pure spinors define Poincaré invariant spheres where quantum problems may be formulated and solved; we will illustrate it for the H-atom stationary states problem, dealt by V. Fock, where the pure spinor sphere (S3) explains the relativistic form of the formula for the energy levels, and suggests further possibilities which are outlined and discussed.