About Non-relativistic Quantum Mechanics and Electromagnetism

We describe here the coherent formulation of electromagnetism in non-relativistic quantum-mechanical many-body theory interacting charged particles. use mathematical frame field and its quantization spirit quantum electrodynamics (QED). This is necessary because a manifold misinterpretations emerged especially regarding magnetic gauge invariance. The situation was determined by historical development mechanics, starting from Schrödinger equation single particle presence given electromagnetic fields, followed theories many identical particles having just Coulomb interactions. Our approach to QED emphasizes role gauge-invariance external fields. develop further approximation this allowing closed description without photons. resulting Hamiltonian coincides with quantized version Darwin containing besides also current-current diamagnetic interaction. show on some examples importance extension theory.