real numbers are sufficient for it. Physicists use it for the description of massive spin-1 particles, such as vector mesons, but its importance for spin theory is much higher because it anchors spin states to the geometry of the physical 3-space. This representation emerged simultaneously with the 2 when William Rowan Hamilton introduced versors, his term for elements of SU(2). Note that Hamilton did not use standard group theory terminology since his work preceded Lie group developments. The (i.e. ) representation is used in particle physics for certain baryons, such as the Δ. See also Rotation operator (vector space) Rotation operator (quantum mechanics) Representation theory of SO(3) Connection between SO(3) and SU(2) representation theory of SL2(R) Electroweak interaction Rotation group SO(3) § A note on Lie algebra References Gerard 't Hooft (2007), Lie groups in Physics, Chapter 5 "Ladder operators" Representation theory of Lie groups Rotation in three dimensions