In
electrodynamics this vector potential
A taken together with the electrical
scalar potential ρ give the four-vector A
μ=(ρ,
A)
T, and the
Maxwell tensor can then be written as F
μν=d
μA
ν-d
νA
μ. Remembering that F
ij=ε
ijkB
k, you can recover the equation that
Blush Response has provided above:
εijlFij = εijlεijkBk = (δjjδkl-δjkδjl)Bk = 2Bi
εijlFij = εijl(djAl-dlAj) = 2εijldjAl
ie.
Which is just
B=
curl A.
The fact that the Maxwell
tensor can be written in terms of the vector potential implies half of
Maxwell's equations - when expressed in the form d
μF
νρ+
d
ρF
μν+
d
νF
ρμ=0. Quite remarkable really.