- Hydrogen atom is problem in QED and therefore also in standard model. The relativistic generalization of hydrogen atom based on Bethe-Salpeter equation does not work properly but predicts a lot of non-existing states. This can be found from the text book or Iztykson-Zuber. Schroedinger equation and Dirac equation give excellent predictions. What goes wrong with QED?
- In superstring theories one cannot say anything about hydrogen atom unless one just assumes that spontaneous compactification yields M4 as base space. It is still unclear whether one really obtains standard model gauge group at low energy limit. Actually one cannot even predict space-time dimension. I do not know whether 3-brane identification can yield the desired QFT limit. Probably not.
- In TGD framework standard model symmetries and fields are coded in CP2 geometry. Standard model and general relativity are obtained at QFT limit when one replaces sheets with single slightly curved region of Minkowski space. Gravitational field (deviation of metric from M4 metric) and gauge potentials are obtained as sums of those for sheets by simple arguments. Effects on test particle touching the sheet sum up at fundamental level and corresponding fields sum up at QFT limit.
- QFT limit of TGD would have same problems as hydrogen atom in QED. That wave mechanics works so well and QED fails must be due to approximation replacing many-sheeted space-time with a region of empty Minkowski space M4. Indeed, in QFT approach one treats proton and electron as disjoint surfaces approximated as point like particles. For bound states they however form single 3-surface obtained by connecting the 3-surfaces by flux tubes. The outcome is too many degrees of freedom and non-physical states as Bethe-Salpeter indeed predicts. In wave mechanics one makes the needed approximation by considering time evolution of wave functions in 3-space instead of 4-D correlation functions and gets rid of spurious states.
For a summary of earlier postings see Latest progress in TGD.