Radiation field integral representation

Operator Al denotes the nonlinear forward modeling operator, given by the Lame equation (15.230) and radiation conditions (13.202) - (13.204). This operator can be calculated, for example, from the general integral representation of the elastic field in the frequency domain (13.97), which we write here in the form... 

The dual representation of the photon operators (67) reflects the transmission of phase information from the atomic transition to the radiation field via the integral of motion (70). This statement can be illustrated with the aid of the Jaynes-Cummings model (34). Employing the atomic phase states (46), we can introduce the dual representation of the atomic operators (35) as follows ... 

The procedure outlined in the Radiated Fields subsection may be followed to find an analytical expression for the uniform current vector potential integral of Eq. (13.66). This results in the following exact series representation for the near-zone of the loop ... 

We have intentionally omitted the details in progressing from Eq. (26-1) to Eq. (26-2) because of their algebraic complexity. Since we only want to show, the formal procedure for decomposing the radiation field, such details are counter-productive from a pedagogical point of view, and are to be found elsewhere [1-3]. Similarly, the approach from the Green s function representation to integrals of the form of Eq. (26-2) is available in Refs. [3,4]. 

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