Dirac Spinor + QED Interaction

Natural units: $\mathbf{c = \hbar = 1}$. Electron mass is set to $\mathbf{m = 1}$. The momentum magnitude is specified by $\mathbf{\beta = |p|/E}$, so $\mathrm{E} = m/\sqrt{1-\beta^2}, p = \beta E$. Angles are in degrees

e-

e+

Hx

H+

H-

Massive

Massless

->

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Spinor 1

β₁:

E₁:

Momentum θₚ₁: °

Momentum φₚ₁: °

Spin θₙ₁: °

Spin φₙ₁: °

e-

e+

Hx

H+

H-

Massive

Massless

->

<-

<=>

Spinor 2

β₂:

E₂:

Momentum θₚ₂: °

Momentum φₚ₂: °

Spin θₙ₂: °

Spin φₙ₂: °

Electromagnetic wave A

|K|:

K θ: °

K φ: °

Polarization angle χ: °
$\chi=0$ gives $e_₁ = \hat{\theta}$; $\chi=90^\circ$ gives $e₂ = \hat{\phi}$. The vector potential is $A_\mu=(0, A\cdot\epsilon)$ at $x=t=0$, with amplitude $|A|=1$.

QED coupling at x = t = 0

We calculate $J^\mu = \bar{u}_2 \gamma^\mu u_1$ and $M = e A_\mu J^\mu$, with $e=1$ and metric $(+---)$. This is the local bilinear corresponding to the interaction term $e A_\mu \bar{\psi} \gamma^\mu \psi$.