Derivation of the fine structure constant using fractional dynamics

Both classical and quantum electrodynamics assume that random fluctuations are absent from the steady-state evolution of the underlying physical system. Our work goes beyond this approximation and accounts for the continuous exposure to stochastic fluctuations. It is known that the asymptotic limit of quantum field dynamics, dominated by large and persistent perturbations, may be described as an anomalous diffusion process. We use fractional calculus as an appropriate tool to handle this highly non-trivial regime. It is shown that the fine structure constant can be recovered from the fractional evolution equation of the density matrix under standard normalization conditions.