TL;DR
This paper reviews the application of noncommutative geometry to the standard model of particle physics, exploring spectral actions, Higgs mass issues, and potential grand symmetry solutions.
Contribution
It provides a comprehensive overview of noncommutative geometric methods applied to particle physics, including new insights into Higgs mass calculations and neutrino roles.
Findings
Spectral geometry framework applied to standard model
Discussion of Higgs mass calculation challenges
Proposal of pregeometric grand symmetry as a solution
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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