Exercise [22.21]

deant · 03 Nov 2012, 14:46

Since the spinorial indices are symmetric, and since they only take the values 0 or 1, the (n+1) independent components of a spinor $\psi$ with n indices are:

$\psi_{000...0}$
$\psi_{100...0}$
$\psi_{110...0}$
$\psi_{111...0}$
.
.
.
$\psi_{111...1}$

As each spin-half direction is represented as a ratio between components, the above (n+1) independent components can be regarded as representing n independent spin-half vectors, which taken together make up the total quantum spin state.