I'm doing some calculations and I've run into something rather strange.
I need to evaluate the following dot products
\vec{\epsilon}_{k,\,s}\cdot\vec{\epsilon}_{-k,\,s'} = ?
\vec{\epsilon}_{k,\,s}^*\cdot\vec{\epsilon}_{-k,\,s'}^* = ?
where \vec\epsilon_{k,\,s} is the normalized...