Hierarchy and Perturbation

[Kirill Danilov]

The reason why the perturbation treatment of quantum mechanics is aided by the multipole expansion in such an investigation of electrodynamics is because the multipole expansion allows for an immediate sense of energy scale hierarchy for the interactions between the charged particles and currents, meaning that the order of perturbation can be easily deduced from the order of the quadrupoles. However, a full treatment of the quantum theory should nonetheless be performed up to all orders via the renormalisation scheme of quantum field theory.

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