Lagrangian for Electromagnetic Interactions

Relativistic Quantum Chemistry. Markus Reiher and Alexander Wolf 

The first term (jCrad) describes the electromagnetic degrees of freedom based on the 4-potential the second ( mat) the Dirac matter field ip, whose excitations may later, i.e., after quantization, be interpreted as electrons and positrons, and the last term ( int) accounts for the interaction between the former two. To write such a Lagrangian goes back to the early days of (the old) quantum electrodynamical theory [103]. 

The gauge field = (p,A) contains the scalar and vector potentials and defines the antisymmetric electromagnetic field tensor f already introduced in section 3.4. A comprises, as before, external, i.e., non-dynamical, electromagnetic potentials in addition to the radiation field. In accordance with section 2.4 the dynamical electric and magnetic fields can be obtained as 

In order to cast the expressions in the simplest possible form, Feynman s slash-notation which we introduced in section 5.2.4, has been em- 

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