  We classify and relate unitary irreducible representations (UIRs) of the
Carroll and dipole groups, i.e., we define elementary quantum Carroll and
fracton particles and establish a correspondence between them. Whenever
possible, we express the UIRs in terms of fields on Carroll/aristotelian
spacetime subject to their free field equations.
  We emphasise that free massive (or "electric") Carroll and fracton quantum
field theories are ultralocal field theories and highlight their peculiar and
puzzling thermodynamic features. We also comment on subtle differences between
massless and "magnetic" Carroll field theories and discuss the importance of
Carroll and fractons symmetries for flat space holography.
