all elements of su(2) can be written as(adsbygoogle = window.adsbygoogle || []).push({});

\exp(iH)

with H being a traceless hermitian matrix

thus H can be written as the sum of \sigma_x,\sigma_y,\sigma_z

H=\theta (n_x \sigma_x + n_y \sigma_y+ n_z \sigma_z).

Here (n_x,n_y,n_z) is a unit vector in R^3.

we can take \theta in the interval (-\pi,\pi]

Thus the su(2) group has the same parameter space as SO(3) group.

what is wrong?

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# Parametrization of su(2) group

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