Lorentz lemma

Now let the radius R of the ball Or tend to infinity. The surface integral over a sphere Cr vanishes due to radiation conditions (8.85) and (8.86), and we arrive at a mathematical formulation of the Lorentz lemma ... 

We now can use the Lorentz lemma to derive the reciprocity relations for the Green s electromagnetic tensor. Let us assume that the electric dipoles with moments a and b are located at points with the radius-vectors r and r",... 

Substituting expressions (8.135) through (8.137) into the Lorentz lemma (8.134), we find... 

The EM Green s tensors exhibit symmetry and can be shown, using the Lorentz lemma, to satisfy the following reciprocity relations (Felsen and Marcuvitz, 1994) ... 

The final result is that the sensitivities can be obtained from the scalar product of the original electric field and the auxiliary electric fields, generated by elementary electric or magnetic dipole current sources, located at the receiver position, r. This result was originally demonstrated by Pellerin et al., 1993, and then a derivation based on Lorentz lemma was given by McGillivray et al., 1994. 

---