Pure Spinor Geometry: Its Possible Role in Quantum Physics

. Recently pure spinor geometry has allowed, after decades of desperate efforts, some definite steps forward for the solution of one of the main unsolved problems of theoretical physics: that of quantum gravity; thus confirming the role of pure spinors in quantum physics. In this paper we try to show that it might be a fundamental role, since pure spinors not only are at the origin of strings, now often adopted in quantum field theory, where they substitute the Euclidean concept of point-event, but also they provide quite simple explanations to several aspects of elementary particle phenomenology, often cumbersome and obscure. Furthermore they naturally define compact manifolds in momentum spaces where a purely geometrical way may be found for the representation and easy solution of some dynamical quantum problems, as first indicated, already a long time ago, by V. Fock.