Noncommutative Geometry and Particle Physics

2018/05/01 by Lizzi, Fedele · 7 citations
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1805.00411

Abstract

We review the noncommutative approach to the standard model. We start with the introduction if the mathematical concepts necessary for the definition of noncommutative spaces, and manifold in particular. This defines the framework of spectral geometry. This is applied to the standard model of particle interaction, discussing the fermionic and bosonic spectral action. The issues relating to the calculation of the mass of the Higgs are discussed, as well as the role of neutrinos and Wick rotations. Finally, we present the possibility of solving the problem of the Higgs mass by considering a pregeometric grand symmetry.

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• Bootstrapping Noncommutative Geometry with Dirac Ensembles
• Feynman spectral action of the wave operator on asymptotically de Sitter spaces
• Unified Pati-Salam from Noncommutative Geometry: Overview and Phenomenological Remarks
• Mixed states for reference frames transformations

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