I am trying to do a simple quantum mechanical calculation that involves both vector and spinor indices. Abstractly, the calculation of the vector $\vec{v}$ looks like the following:
The right-most object involves the contraction of quantum states $\psi$ and $\phi$ with the $x,y,z$ Pauli matrices $\boldsymbol{\sigma}_{x,y,z}$. I use the bold (but it's hard to see) to indicate abstract quantum operators and the vector to indicate having three components for three spatial coordinates ${x,y,z}$.
In any case, you can accomplish this calculation by first using a matrix representation to evaluate the right-most object like:
Then, we can easily take the cross product with $\vec{q}$ of the resulting expression with only vector indices.
What I'm looking for is a way to set this up in Mathematica as either my own library or an existing library that can easily handle many such calculations without me needing to "unpack" things much further than the abstract notation in my first equation. Does something like this exist?
I am aware of the library suggested here but that's for what seems to be more detailed calculations than I am doing and I can't decide if the overhead of learning is worth it.
