Coupling of space-time and electromagnetic gauge transformations

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Abstract
A kind of topological extensions of a space-time group Q by an electromagnetic gauge group J are investigated in order to determine covariance groups of electrodynamics. Here Q stands for the Poincaré group, for the Galilei group, or for their neutral components, and J is the Abelian group of all real-valued functions of class Cm (m ∈ N or m = ∞) defined in space-time. The topological groups JφfQ so obtained, already important in the study of charged particles in external electromagnetic fields, are analyzed and placed in the general context of combining different symmetry groups. They are characterized by a given operation φ of Q on J and by factor sets f such that f(q,q′) is a constant gauge function for all (q,q′) ∈ Q × Q. It is shown that all these groups JφfQ are topologically isomorphic to the external topological semidirect product of Q by J relative to Φ.

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