Cooper Pair Formation by Quantizing Brownian Motion

We derive a new quantum interaction by quantizing the Brownian motion based on the Nelson equations. By applying the canonical quantization for the equations, interaction as the connection of Brownian and quantum motions appears. Interesting aspect is that it can overcome the Coulomb repulsion if the diffusion coefficient is large enough. As the parameters are mass, diffusion coefficient, and probability density, we can calculate and predict the Cooper pair formation with measurable variables.