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.