Lagrangian and Hamiltonian Formalism in Unified Fractal Quantum Field Theory (UFQFT)

In this work, we develop the Lagrangian and Hamiltonian formalism for the Unified Fractal Quantum Field Theory (UFQFT), a framework in which all particles are described as resonance configurations of energy (Φ) and charge (Ψ) fields in a fractal spacetime with dimension D≈2.7. We present the general structure of the UFQFT Lagrangian, including free field and interaction terms, and derive the corresponding Hamiltonian for canonical quantization. The formalism naturally reproduces particle oscillations, such as neutrino flavor transitions and quark mixing, via phase-resonance matrices analogous to the PMNS and CKM matrices of the Standard Model. Conservation laws and symmetries are analyzed in the context of fractal spacetime, and implications for particle stability and decay processes are discussed. This approach provides a geometrical and dynamical foundation for weak and flavor interactions, offering a unified framework for the description of elementary particles and their transitions.