Interaction of quantized fields

The unique practical way to describe the theory of the interacting fields is by perturbation theory (PT). This is most justified for QED where the coupling parameter is a (see Introduction). The perturbation theory is most conveniently developed within the Hamilton formalism. Therefore we present the total Hamiltonian for the interacting electron-positron and electromagnetic fields as 

By analogy with the classical interaction the interaction Hamiltonian should be  

The Hamiltonian (103), as well as the Hamiltonians (101) and (102) is defined in the Fock space. In the Fock space it is possible to write down the Schrodinger equation for the interacting fields  

The PT is developed then as the iterative solution of Eq(109). Combined with the condition  

For general purposes it is more convenient to go over the symmetrized form of the expression (112)  

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