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Résumé |
Given a kinematical group G (such as Poincar\'e, Galilei, Carroll,...), Souriau gave a mathematical definition of a classical particle: a homogeneous symplectic manifold of G. This postdates Wigner's definition of a quantum elementary particle: a projective unitary irreducible representation of G. The determination of classical and quantum particles of Poincaré and to some extent Galilei is largely well-known, but the Carroll case is more recent. In this talk I aim to summarise joint work with Alfredo P\'erez and Stefan Prohazka on the determination of classical and quantum particles of the Carroll group and, also with Simon Pekar, of the Galilei group. If time allows, I will comment on their application to the study of fractons and planeons. |
