Exact Results in Quantum Theory

I will present a derivation of the Schrodinger equation for twocharged particles from Quantum Electrodynamics (QED).First I compute renormalized Hamiltonian of QED, whichacts in whole Fock space. Then I reduce it using Wilsonianrenormalization group procedure to the sector with onlytwo charged particles and obtain the Schrodinger equation."Off-shell" means that energy in the interaction is notconserved, which is contrasted with the textbook procedurethat is based on energy-conserving scattering. Moreover,renormalized particles have a nonzero size, hence, the off-shellpotential differs slightly from the classical Coulomb potential.