Noncommutative Algebra Papers
Research publications on spectral geometry, TSQVT, the Standard Model from spectral action, and noncommutative geometry by Kerym Makraini.
UNED National University of Distance Education, Madrid, Spain
AGE Quantum Gates Engine S.L., Melilla, Spain
Peer-Reviewed Publication
Emergent Lorentzian Spacetime and Gauge Dynamics from Twistorial Spectral Data
By Kerym Makraini
We introduce the Twistorial Spectral Quantum Vacuum Theory (TSQVT), a Lorentzian background-independent framework where spacetime and gauge fields emerge from twistorial spectral data on a Krein space. A spectral density ρ acts as order parameter: its condensed regime generates the conformal metric without prior geometric input, resolving the geometry-matter circularity.
Preprints (11)
Three Fermion Generations from Spectral Geometry: Dynamical, Algebraic, and Vacuum Constraints
We show that the number of fermion generations is constrained by spectral–geometric principles and satisfies the strict, model–independent bound N_gen ≤ 3. The KO–dimension 6 finite algebra A_F = C⊕H⊕M₃(C) admits exactly three minimal central idempotents. We introduce a dynamical Spectral Exclusion Principle (SEP) enforcing one-to-one correspondence between vacuum minima and fermionic sectors.
Spectral Geometry of the Standard Model Algebra: Trace Structures and Gauge Unification
We present a complete derivation of the gauge unification condition sin²θ_W = 3/8 within the spectral geometry framework of Connes and Chamseddine. Working with the finite algebra A_F = C⊕H⊕M₃(C), we compute the trace invariants controlling the spectral coefficients. The key result—C_U(1)/C_SU(2) = 1/3—follows from explicit trace calculations over the fermionic representation space.
Spectral Higgs Portal: Falsifiable TeV Predictions from Twistor Geometry
A spectral-action–derived Higgs portal predicts a heavy scalar with fixed portal strength and a distinctive collider signature. The portal coupling emerges from the heat-kernel expansion, with α₁ ≃ 4.3×10⁻² numerically dominated by the top sector. Combining Higgs precision constraints yields a narrow mass window m_ρ ∈ [2.0, 3.5]TeV. We predict σ×BR(ρ→WW) ≃ 1.0–1.5fb at the HL-LHC.
The ρ-Higgs Portal in TSQVT: Predictions for TeV-Scale Collider Searches
We derive a unique scalar collective mode ρ as the spectral condensation order parameter of TSQVT. From the heat-kernel expansion of the twistorial spectral action we derive the portal interaction βρ|H|² and compute all coefficients in terms of spectral moments. Electroweak symmetry breaking is induced without introducing ad hoc scalar parameters.
On the Necessity of Internal Degrees of Freedom in Conformally Invariant Structures
We analyze the logical structure of conformally invariant field theories, motivated by Penrose's observation on spectral splitting. Recasting the frequency distinction in terms of holomorphic extension on twistor space yields a conformally invariant criterion. We introduce the conformal density parameter ρ with rigorous cohomological definition based on regularized Dolbeault traces.
Emergence of Conformal Geometry and Einstein Equations in the Conformal Sector
We define the concept of a twistorial vacuum as the base state of a conformally invariant complex structure, characterized by maximal holomorphic regularity. We show that pseudo-Riemannian geometry emerges as a consistency condition for perturbations of the twistorial vacuum, with Einstein field equations arising as the leading-order constraint.
Gravity from the Structural Intensity Field ρ: A Real-Time Spectral Framework
We present a precise, coordinate-free definition of the structural intensity field ρ and use it as the primary geometric variable in real time. The construction is supported by: an adiabatic twistor collapse selecting the anti-selfdual sector, a noncommutative Penrose–Ward correspondence, and a time–space no-go theorem enforcing θ₀i = 0.
A Spectral Exclusion Principle for Emergent Spacetime from a Non-Commutative Twistor Geometry
This paper introduces a novel framework for a unified theory of quantum gravity, derived from the axiomatic definition of a mathematical structure termed the Non-Commutative Twistorial Quadruplet (NCTQ). Spacetime is not fundamental but an emergent phenomenon governed by a Spectral Exclusion Principle.
A Rigorous Formulation of the Twistor-Structural Quantum Vacuum: Hermiticity, Derivations, and Experimental Constraints
We present a rigorous formulation of TSQVT, establishing: a manifestly self-adjoint Hamiltonian for particles with position-dependent effective mass, a toy model based on a static source in twistor space yielding analytic solutions for ρ(x), and phenomenological constraints from high-precision hydrogen spectroscopy.
The Structural Abolition of Fine-Tuning: A Twistor-Spectral Solution to the Higgs Hierarchy Problem
The hierarchy problem of the Higgs boson represents a profound conceptual crisis. We introduce TSQVT, whose central axiom asserts that spacetime is an emergent scalar field ρ(x). Within this framework, the Higgs potential and mass are derived quantities emerging from the spectral action—conceptually dissolving the fine-tuning paradox.
A Spectral-Geometric Solution to the Yang-Mills Mass Gap Problem via TSQVT
We present a complete resolution of the Yang-Mills Existence and Mass Gap Millennium Problem. The field equations for ρ(x) admit stable, localized solutions called 'geometric bags', where spacetime intensity collapses to zero. This induces geometric confinement trapping Yang-Mills modes with a strictly positive mass gap Δ > 0.