So, using the Dirac spinor notation for plane-wave electrons and positrons from HERE, and the definition of the adjoint of $\psi$ = $\psi^{*T} \gamma^0$, and applying that to the "up" electron (with the Dirac version of $\gamma^0$), I get

$\bar{\psi} = e^{ip\cdot x} [ 1 \space 0 \space -p_z/(E+m) \space \space (-p_x+ip_y)/(E+m)]$

The vector part is the same as the original electron's vector, with $p_x$ and $p_z$ reversed, but not $p_y$. In addition, the exponent term now represents "negative energy", or an anti-particle. But the momentum term's positions in the vector are for those of a particle.

How is this to be interpreted physically? In other words, what kind of particle (if any) does it represent?


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