More on Rotations as Spin Matrix Polynomials

Abstract

Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of biorthogonal systems is a useful framework to meet this challenge. Central factorial numbers play a key role in the theoretical development. Explicit polynomial coefficients for rotations expressed either as exponentials or as rational Cayley transforms are considered here. Structural features of the results are discussed and compared, and large j limits of the coefficients are examined.

Additional references, simplified derivation of Cayley transform polynomial coefficients, resolvent and exponential related by Laplace transform. Other minor changes to conform to published version to appear in J Math Phys

References in corpus (3)

• A Compact Formula for Rotations as Spin Matrix Polynomials
• Supersymmetric Biorthogonal Quantum Systems
• On Rotations as Spin Matrix Polynomials

Cited by in corpus (3)

• Elementary results for the fundamental representation of SU(3)
• Matrix exponentials, SU(N) group elements, and real polynomial roots
• Complete Population Transfer of Maximally Entangled States in $2^{2N}$-level Systems via Pythagorean Triples Coupling