A Compact Formula for Rotations as Spin Matrix Polynomials

Abstract

Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. The simple explicit result exhibits connections between group theory, combinatorics, and Fourier analysis, especially in the large spin limit. Salient intuitive features of the formula are illustrated and discussed.

Cited by in corpus (11)

• Topology and entanglement in quench dynamics
• Elementary results for the fundamental representation of SU(3)
• i-SPin 2: An integrator for general spin-s Gross-Pitaevskii systems
• Matrix exponentials, SU(N) group elements, and real polynomial roots
• On Rotations as Spin Matrix Polynomials
• Solving the spin-2 Gross-Pitaevskii equation using exact nonlinear dynamics and symplectic composition
• More on Rotations as Spin Matrix Polynomials
• Spin-selective Aharonov-Casher caging in a topological quantum network
• SU(2) hyper-clocks: quantum engineering of spinor interferences for time and frequency metrology
• Spin-dependent edge states in two-dimensional Dirac materials with a flat band
• Complete Population Transfer of Maximally Entangled States in $2^{2N}$-level Systems via Pythagorean Triples Coupling