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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.05909 |
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Table of Contents:
- This article surveys the noncommutative-geometric (NCG) approach to fundamental physics, in which geometry is encoded spectrally by a generalized Dirac operator and where dynamics arise from the spectral action. I review historically how the simple idea of marrying a Riemannian manifold to a two point space, progressed to lead to the uniqueness of the Standard Model and beyond. I explain how inner fluctuations of the Dirac operator reconstruct the full gauge-Higgs sector of the Standard Model on an almost-commutative space, fixing representations and hypercharges and naturally accommodating right-handed neutrinos and the see-saw mechanism. On the gravitational side, the heat-kernel expansion of the spectral action yields the cosmological constant, Einstein--Hilbert term, and higher-curvature corrections, with volume-quantized variants clarifying the status of $Λ$. I discuss the renormalization-group interpretation of the spectral action as a high-scale boundary condition, phenomenological implications for Higgs stability and neutrino masses. I present generalized Heisenberg equation leading to identify the NCG space at unification. I conclude by emphasizing that NCG provides a unified, testable, and geometrically principled quantum framework, linking matter, gauge fields, and gravity.