This link provides a short introduction to the contributions of Uhlenbeck about regular gauge fixing. However, I feel quite puzzled about it and I do not understand the real novelty apported by this work. More concisely, it would be helpful for me to understand
which is the transcendence and novelty of the local Coulomb gauge theorem (theorem 3.2), in case it can be shortly explained, and what it is useful for.
which relation has this result with physics (I have heard in the web that the so-called $\epsilon$ plays some Planck's constant role, and that everything may be translated into quantum physics, or at least physics world).
Any suggestion for those two questions will be welcomed.