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point charge (see [25] for a more detailed explanation if needed) 

Here the argument 0 of the Green function stands for k$_{0}$ . Among the basic vectors (31) there is only one whose fourth component remains nonzero in the static limit k$_{0}$ = 0. It is c + $_{µ}$. It participates in the eigenvectors ♭ (2 , 3) µ in accord with (10). Hence only these two eigenvectors will remain in the decomposition (28) of D after it is substituted into (39). On the other hand the contribution of the basic vector c − µ may only supply the spacial components to the vector-potential (39), whereas c + µ cannot. Bearing in mind that eqs. (31) imply in the static limit, k$_{0}$ = 0, that 

the spacial part of the latter is 

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To find the large distance behavior of this field note that it is determined by the limit k = 0 in the pre-exponential factor in the integrand. Therefore, we set κ 2 , 3 = 0 and use eq. (20) for Λ$_{3}$ 

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Then 

This vector in the two-dimensional plane orthogonal to the external fields is directed as [x$_{⊥}$ × ϵ ] , since the coordinate vector x$_{⊥}$ in that plane fixes the only direction on which the integral may depend. The length of (43) 

decreases via the Coulomb law with the radial distance | x | from the charge. The vector potential and the magnetic field carried by it at large distances are 

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