Negative Energy, Screw It

There is no need to define negative energy nor negative time,

just opposing spins, given the right hand screw rule.  The sign in the expression,

$i\cfrac{\partial\,\psi_{t_g}}{\partial\,x_1}$

for the diagram on the left changes to,

$-i\cfrac{\partial\,\psi_{t_g}}{\partial\,x_1}$

with opposite spin, as the diagram on the right.

In both cases, $x_1$ serve as the radius of the cross section circle perpendicular to $x_2$, the direction of travel of the particle.  $i$ rotates $x_1$, $\pi/2$ anti-clockwise into the perpendicular direction and the expression denotes the change in $\psi_{t_g}$ in the direction perpendicular to $x_1$, in the plane containing the circle that defines the spin.

The diagram on the left with a anti-clockwise spin is a photon, as we know them.