# Spinor representation of rotation

1. Apr 4, 2013

### raopeng

1. The problem statement, all variables and given/known data
Show the spinor representation corresponding to the rotation through an angle θ about an axis with direction vector $n = (n_x, n_y, n_z)$ has the form: $g=exp{-i\frac{θ}{2}(n_x σ_x+n_yσ_y+n_zσ_z)}, σ_{x, y, z}$ are respectively Pauli matrix

2. Relevant equations
$h=gxg^{-1}$

3. The attempt at a solution
Since pauli matrices span the matrix space, I try to interpret the three pauli matrices as basis in a vector space. Then following from the knowledge of Euler Angle the spinor representation is indeed of that form. But this approach seems nowhere close to mathematical rigour as it is in a geometry book.