Events and cosmological spaces through twistors in the geometric (Clifford) algebra formalism

Abstract

Events in Minkowski space-time can be obtained from the intersection of two twistors with no helicity. These can be represented within the geometric (Clifford) algebra formalism, in a particular conformal space that is constructed from a quantum system of two particles. The realisation takes place in the multiparticle space-time algebra. This representation allows us to identify an event with the wave-function for a non-charged Klein-Gordon particle. A more general point can also be obtained, if the space is complexified and the twistors have non-zero helicity. In this case, such a point is no longer an event, but it can be identified with the wave-function for a charged Klein-Gordon particle. Other spaces of cosmological relevance can also be constructed using the 2-particle representation of the conformal space, as is the case for de Sitter and anti-de Sitter spaces. Furthermore, we show that Friedmann-Robertson-Walker spaces, with and without big bang, are fully described through two twistors, which are expressed within our formalism in terms of entities belonging to quantum mechanics: the Dirac matrix $\gamma_0$, a massless maximally entangled state and its complex conjugate.