Abstract
Following the work of C. B. van Wyk on the Lorentz
group SO(3, 1), we first express a general finite rotation of SO(4)
in terms of 2 ordinary (3-dimensional) vectors a and b satisfying
certain conditions and then using the homomorphism of SU(2) ×
SU(2) onto SO(4), we express the same rotation in terms of a pair
of 2 × 2 matrices, again determined by the same pair of vectors a
and b. This is extremely useful as it allows one to convert the 4 × 4
matrix multiplication of elements of SO(4) into the 2 × 2 matrix
multiplication of elements of SU(2).
Muneer Ahmad Rashid (Rtd.), Ansaruddin Syed. (2017) Spinor Representation of Finite Rotations of SO(4), Punjab University Journal of Mathematics, Volume 49, Issue 1.
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