2015/04/15 by Christian Brouder, Brouder, Christian, Nadir Bizi +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.48550/arxiv.1504.03890
The new version includes the Standard Model with a Lorentzian signature
openalex publication_date 2015/04/15 · arxiv created 2015/06/05 · arxiv updated 2015/06/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
The Standard Model of particle physics can be deduced from a small number of axioms within Connes' noncommutative geometry (NCG). Boyle and Farnsworth [New J. Phys. 16 (2014) 123027] proposed to interpret Connes' approach as an algebra extension in the sense of Eilenberg. By doing so, they could deduce three axioms of the NCG Standard Model (i.e. order zero, order one and massless photon) from the single requirement that the extended algebra be associative. However, their approach was only applied to the finite algebra and fails the full model. By taking into account the differential graded structure of the algebra of noncommutative differential forms, we obtain a formulation where the same three axioms are deduced from the associativity of the extended differential graded algebra, but which is now also compatible with the full Standard Model. Finally, we present a Lorentzian version of the noncommutative geometry of the Standard Model and we show that the three axioms still hold if the four-dimensional manifold has a Lorentzian metric.