Contractions Of The Maxwell Algebra

We construct all the possible non-relativistic, non-trivial, Galilei and Carroll k-contractions also known as k-1 p-brans contractions of the Maxwell algebra in D + 1 space-time dimensions. k has to do with the number of space-time dimensions one is contracting. For non-trivial solutions, we mean the ones with a non-abelian algebra of the momenta. We find, in both cases, Galilei and Carroll, eight non-trivial solutions. We also study the electromagnetic properties of the solutions, defined according to the scaling performed on the generators present in the Maxwell algebra. We find that besides the electric and magnetic contractions studied in the literature for k = 1, that are related to the magnetic and electric limit of the free Maxwell equations, contractions also exist where the two types of fields are scaled in the same way.