Pure Spinor Geometry: Its Possible Role in Quantum Physics

Abstract

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.