Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 024, 24 pages      arXiv:2206.11138      https://doi.org/10.3842/SIGMA.2023.024

Some Useful Operators on Differential Forms on Galilean and Carrollian Spacetimes

Marián Fecko
Department of Theoretical Physics, Comenius University in Bratislava, Slovakia

Received August 30, 2022, in final form April 11, 2023; Published online April 22, 2023

Abstract
Differential forms on Lorentzian spacetimes is a well-established subject. On Galilean and Carrollian spacetimes it does not seem to be quite so. This may be due to the absence of Hodge star operator. There are, however, potentially useful analogs of Hodge star operator also on the last two spacetimes, namely intertwining operators between corresponding representations on forms. Their use could perhaps make differential forms as attractive tool for physics on Galilean and Carrollian spacetimes as forms on Lorentzian spacetimes definitely proved to be.

Key words: Hodge star operator; Galilean spacetime; Carrollian spacetime; intertwining operator.

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