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UFQFT Lagrangian and Emergent Gauge Symmetries: Recovering the Mathematical Foundations of the Standard Model from Resonance Geometry

Authors: sogukpinar, haci;

UFQFT Lagrangian and Emergent Gauge Symmetries: Recovering the Mathematical Foundations of the Standard Model from Resonance Geometry

Abstract

The Standard Model of particle physics is one of the most successful theories in modern science,accurately describing elementary particles and their interactions through the gauge symmetry groupU(1)×SU(2)×SU(3). Despite its remarkable predictive power, several fundamental questions remainunresolved, including the origin of mass hierarchies, the nature of dark matter and dark energy, theabsence of a quantum theory of gravity, and the deeper physical origin of gauge symmetries themselves.In this work, we investigate whether the mathematical foundations of the Standard Model can emergenaturally within the framework of Unified Fractal Quantum Field Theory (UFQFT). UFQFT describesphysical reality in terms of two fundamental fields, the energy field Φ and the charge field Ψ, embeddedin a fractal spacetime characterized by a critical dimension (Dc=2.7). Starting from a generalized actionprinciple and a fractal variational formalism, we derive conservation laws, generalized Noether currents,and resonance-based symmetry structures. We demonstrate how U(1)-like, SU(2)-like, and SU(3)-likesymmetries can arise as emergent manifestations of resonance geometry rather than being introduced asfundamental gauge postulates. The correspondence between UFQFT and the Standard Model isexamined through the recovery of effective gauge structures in the weak-fractal and low-energy limits.We further compare the conceptual foundations of both frameworks, emphasizing the transition fromgauge geometry to resonance geometry. The results suggest that gauge symmetries may representeffective large-scale descriptions of deeper resonance dynamics governed by coupled Φ–Ψ fields in acritical fractal spacetime. This work constitutes the first systematic attempt to establish the mathematicalcorrespondence between UFQFT and the Standard Model and provides a foundation for futuretheoretical and experimental validation studie

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