Some useful operators on differential forms in Galilean and Carrollian spacetimes

Marián Fecko

Published 2022-06-22Version 1

Differential forms in Minkowski spacetime is a folklore subject. In Galilean and Carrollian spacetimes it does not seem to be quite so. This might be caused by absence of Hodge star operator. There are, however, useful analogs of Hodge star operator also in the two spacetimes, namely intertwining operators between corresponding representations on forms. Their use could make differential forms as interesting tool for writing down Galilean and Carrollian invariant equations as forms in Minkowski spacetime are known to be for writing down (as well as manipulating) Poincar\'e invariant equations.