point charge (see [25] for a more detailed explanation if needed) A$_{µ}$ ( x ) = q (2 π ) 3 ∫ D$_{µ}$$_{0}$ (0 , k ) exp( − i kx )d $^{3}$k. (39) 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 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$_{3}$ 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 21 A ( x$_{⊥}$ , x$_{3}$ ) | | x |→∞ ≃ [x$_{⊥}$ × ϵ ] | x$_{⊥}$ | q M 8 π 1 | x | , h$_{3}$ = q M 8 π ( 1 | x || x$_{⊥}$ | − | x$_{⊥}$ | x | 3 ) , h$_{⊥}$ = q M 8 π x$_{⊥}$ | x$_{⊥}$ | x$_{3}$ | x | $_{3}$. (45) | A | | x |→∞ ≃ q M 8 π 1 | x | . (44) A ( x$_{⊥}$ , x$_{3}$ ) | | x |→∞ ≃ q M (2 π ) 3 ∫ i k$_{3}$ [k$_{⊥}$ × ϵ ] exp( − i kx )d $^{3}$k k 4 . (43) Λ$_{3}$ | k$_{µ}$ → 0 = i | k$_{⊥}$ | k$_{3}$ M , M = L$_{FG}$ ( B 2 + E $^{2}$) − ( L$_{GG}$ + L$_{FF}$ ) G . (42) A$_{i}$ ( x ) = q (2 π ) 3 ∫ ∑ a =2 , 3 ♭ ( a ) i ♭ ( a ) 0 ( ♭ ( a $^{)}$)2 exp( − i kx )d $^{3}$k k 2 κ a = q (2 π ) 3 ∫ c − i Λ$_{3}$ exp( − i kx )d $^{3}$k ( k 2 − κ $_{2}$)( k 2 − κ $_{3}$) , i = 1 , 2 A$_{3}$ ( x ) = 0 . (41) c + i = c − 0 = 0 , c + 0 = 1 , c − i = [k$_{⊥}$ × ϵ ]$_{i}$ | k$_{⊥}$ | , i = 1 , 2 , c ± 3 = 0 (40)