Moller scattering
Definition: Moller scattering
Moller scattering is the process in scalar QED.
To calculate the
Cross sections
In quantum field theory we can predict matrix elements which lead to probabilites of a state evolving into...Cross sections
There are two possible diagrams. They are classified according to the momentum transfer in terms of the
Mandelstam variables
The Mandelstam variables are lorentz invariant kinematic variables used mostly in processes:
Definition: Mandelstam variables
> The Mandelstam variables for...Mandelstam variables
# t-channel:
The momentum transfer is , so that
Inserting the photon propagator and the proper vertex factors gives:
Pasted image 20230915193349.png
Note that because the dependence vanishes. This is expected and neccessary because of gauge invariance, no final results should depend on the choice of gauge
The final result is
# u-channel:
For the u-channel the momentum transfer is giving
Pasted image 20230915193318.png
Again the gauge dependence vanishes
The final result is
From $\mathcal{M}=\mathcal{M}_t + \mathcal{M}u$ we get the final expression for the
Cross sections
In quantum field theory we can predict matrix elements which lead to probabilites of a state evolving into...Cross sections