Maxwell's equations in four-dimensional notation and the classical magnetic monopoles

It is shown that, on account of the commutability of the order of derivation of the electromagnetic 4-potential, the first pair of Maxwell equations, when written in a four dimensional notation, is incompatible with the existence of the classical magnetic monopole. It is hypothesized that the appearance in the past of magnetic monopoles could be accepted only if, in exceptional occurrences, it came to be locally lacking the space homogeneity and isotropy on which the commutability of space derivatives is based. The situation is more complex for massive cosmological monopoles. (C) 2014 Elsevier B.V. All rights reserved.