This question pertains to some notation in Zee's QFT book, Section II.2. The Dirac equation is
$$ (i\gamma^\mu\partial_\mu-m)\psi(x)=0, $$
which we can write in momentum space with the Fourier transform
$$ \psi(x)=\int\!\frac{d^4p}{(2\pi)^4}e^{-ipx}\psi(p)$$
as
\begin{align} (i\gamma^\mu\partial_\mu-m)\int\!\frac{d^4p}{(2\pi)^4}e^{-ipx}\psi(p)&=0\\ \int\!\frac{d^4p}{(2\pi)^4}(\gamma^\mu p_\mu-m)e^{-ipx}\psi(p)&=0\\[8pt] \implies(\gamma^\mu p_\mu-m)\psi(p)&=0, \end{align}
which is the Dirac equation in momentum space. In the rest frame, $p_i=0$ and $p_0=m$ so we have
$$ (\gamma^\mu p_\mu-m)\psi(p)=(\gamma^0p_0+\gamma^ip_i-m)\psi(p) =0\quad\implies\quad(\gamma^0-1)\psi(p)=0.$$ For two Dirac bispinors $u$ and $v$, the solutions are
$$\psi(p)=u(p,s)e^{-ipx}~~,\quad\text{and}\qquad \psi(p)=v(p,s)e^{ipx}.$$
We define $\bar u=u^\dagger\gamma^0$ and $\bar v=v^\dagger\gamma^0$, with dagger denoting the conjugate transpose, to form Lorentz invariants $\bar uu$ and $\bar vv$. Now I have gotten to my question. Zee gives a rest frame identity
$$ \sum_s u_\alpha(p,s)\bar u_\beta(p,s)=\left( \begin{matrix} 1&0&0&0\\0&1&0&0\\0&0&0&0\\0&0&0&0\end{matrix} \right)_{\!\alpha\beta}. $$
If it's not the spin $s$, which it is clearly not, then what do the $\alpha,\beta$ subscripts refer to? Is it two discrete positions $\alpha$ and $\beta$? What is the meaning of the subscript $\alpha\beta$ on the matrix? Does that turn it into a Kronecker matrix?
