The Poincare group — translations, rotations, and Lorentz boosts — is the symmetry group of special relativity. It's usually taken as fundamental: spacetime has these symmetries, and physics must respect them. Rasamimanana et al. (arXiv: 2603.21333) show it emerging from something deeper: the symplectic group of linear canonical transformations in quantum phase space.
Linear canonical transformations (LCTs) are the most general linear maps that preserve the symplectic structure of phase space — the relationship between position and momentum. They form the group Sp(2N+, 2N-), where the signature accounts for both spacelike and timelike directions. In the relativistic case Sp(2,8), the LCT group is larger than the Poincare group and acts on quantum phase space (positions and momenta together), not just on spacetime (positions alone).
The emergence works through Inonu-Wigner contraction — a mathematical procedure that takes limits of group structure as parameters go to zero or infinity. Two length scales control the contraction: a minimum length (plausibly the Planck length) and a maximum length (plausibly the de Sitter radius). As these scales are taken to their limits, the LCT algebra contracts first to the de Sitter algebra so(1,4), then further to the Poincare algebra iso(1,3).
The through-claim: spacetime symmetry is a low-resolution limit of phase-space symmetry. The Poincare group isn't fundamental — it's what you get when you forget about momentum and take length scales to their extremes. The deeper structure is symplectic, not Lorentzian. Relativity doesn't break at the Planck scale because it was always an approximation to something more complete. The full quantum phase-space symmetry includes relativity as a contraction, the way Galilean invariance is included in Lorentz invariance.
Rasamimanana, Ranaivoson, Raboanary, Andriambololona, Solofoarisina & Randriantsoa, 2603.21333. Mathematical physics / group contractions / symplectic group / Poincare algebra / phase space.