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We presented a new physical model that links the maximum speed of light withthe minimal Planck scale into a maximal-acceleration Relativity principle inthe spacetime tangent bundle and in phase spaces (cotangent bundle). Themaximal proper-acceleration bound is a = c^2/ \Lambda in full agreement withthe old predictions of Caianiello, the Finslerian geometry point of view ofBrandt and more recent results in the literature. Inspired by themaximal-acceleration corrections to the Lamb shifts of one-electron atoms byLambiase, Papini and Scarpetta, we derive the exact integral equation thatgoverns the Renormalization-Group-like scaling dependence of the fractionalchange of the fine structure constant as a function of the cosmologicalredshift factor and a cutoff scale L_c, where the maximal accelerationrelativistic effects are dominant. A particular physical model exists dominatedentirely by the vacuum energy, when the cutoff scale is the Planck scale, with\Omega_\Lambda \sim 1 . The implications of this extreme case scenario arestudied.Comment: Latex file, 24 pages, corrected versio

ON THE VARIABLE FINE STRUCTURE CONSTANT, STRINGS AND MAXIMAL-ACCELERATION PHASE SPACE RELATIVITY