A Novel Relativistic Force Formula. Derivation and Applications in High-Energy Dynamics

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Research Paper (undergraduate) from the year 2026 in the subject Didactics - Physics, , language: English, abstract: This paper derives a novel force formula from a relativistic Lagrangian incorporating gamma functions and inverse tangent terms, yielding F = (2 m_0 a / ¿) tan^{-1} [ (¿ / 2) (1 + a^2 / c^2)^n ¿(1 + a/¿) / ¿(1 - a/¿) ]. Unlike standard special relativity's divergent ¿^3 m_0 a, this expression saturates at high energies, modeling bounded interactions in quark-gluon plasmas or metamaterials. Derivation from action principles ensures Lorentz covariance. Limits recover Newtonian mechanics and cap ultra-relativistic forces. Numerical examples and comparisons demonstrate 15-25% deviations in TeV regimes, suggesting applications in particle accelerators and nonlinear field theories.

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