What question did this study set out to answer?

To derive the gauge unification condition sin2 θW = 3/8 using the spectral geometry framework.

January 22, 2026Open Access

Spectral Geometry of the Standard Model Algebra: Trace Structures and Gauge Unification

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This research derives the gauge unification condition in the Standard Model using spectral geometry, suggesting new insights into particle physics.

To derive the gauge unification condition sin2 θW = 3/8 using the spectral geometry framework.
Derived gauge condition using spectral geometry of Connes and Chamseddine.
Worked with the finite algebra AF = C ⊕ H ⊕ M3(C) to encode the Standard Model structure.
Calculated trace invariants related to spectral coefficients affecting gauge terms.
Achieved the ratio CU(1)/CSU(2) = 1/3 from trace calculations.
Predicted sin2 θW(MZ) ≈ 0.231, aligning with precision electroweak data.

Mohamed Makraini (2026) studied this question.

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This research derives the gauge unification condition in the Standard Model using spectral geometry, suggesting new insights into particle physics.