Electrodynamics with a Quantum of Length

Generalized from the work of Yan, electrodynamics with a length quantum is developed at the level of classical mechanics and ordinary quantum mechanics. In this theory, the length quantum λ is a space-time distance over which operators and field variables are averaged. No space-time granularity or any other departure from special relativity is introduced. However, the free-particle wave equation may be expressed as a difference equation. For λ even as large as 10^-13 cm, effects on low-energy electron phenomena (magnetic moment, Lamb shift, and fine structure) are negligible. For λ5×10^-16 cm, a perceptible shift of the muon magnetic moment is predicted. Other consequences, especially at high energy, remain to be explored, as does the second-quantized version of the theory.