- #1
wdlang
- 307
- 0
all elements of su(2) can be written as
\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?
\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?