Classification of Corrections

The zero-order effective Dirac equation with a Coulomb source provides only an approximate description of loosely bound states in QED, but the spectrum of this Dirac equation may serve as a good starting point for obtaining more precise results. 

Each of the small parameters above plays an important and unique role. In order to organize further discussion of different contributions to the energy levels it is convenient to classify corrections in accordance with the small parameters on which they depend. 

Corrections which depend only on the parameter Za will be called relativistic or binding corrections. Higher powers of Za arise due to deviation of 

Eides et al. Theory of Light Hydrogenic Bound States, STMP 222, 13—18 (2007) 

Contributions to the energy which depend only on the small parameters a. and Za. are called radiative corrections. Powers of a arise only from the quantum electrodynamics loops, and all associated corrections have a quantum field theory nature. Radiative corrections do not depend on the recoil factor m/M and thus may be calculated in the framework of QED for a bound electron in an external field. In respective calculations one deals only with the complications connected with the presence of quantized fields, but the two-particle nature of the bound state and all problems connected with the description of the bound states in relativistic quantum field theory still may be ignored. 

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