Heisenberg Operators in Quantum Electrodynamics. II

The equations of motion of quantum electrodynamics are set up in the interaction representation, using a formalism due to Gupta. A new representation, called the intermediate representation, is defined by constructing explicitly a unitary operator $S\left(t\right)\mathrm{}$, which transforms the state-vector of the interaction representation into the state-vector of the new representation. The intermediate representation is intermediate in behavior between the interaction and Heisenberg representations. In it the low frequency changes in the state of a system are represented by changes in the state-vector, as in the interaction representation, while the high frequency fluctuations are represented by the time-variation of the field operators, as in the Heisenberg representation.