2006/04/20 by Elsa Arcaute, A. Lasenby, Anthony Lasenby +4
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic and Geometric Analysis #Clifford algebra #FOS: Physical sciences #Formalism (music) #Geometric algebra #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Physics #Pure mathematics #Theoretical physics #Universal geometric algebra #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0604048
25 pages, no figures. Typos and presentation revised
openalex publication_date 2006/04/20 · arxiv created 2006/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 γ0, a massless maximally entangled state and its complex conjugate.