# Scattering Amplitude

In the Møller scattering we have identical particles in the initial and final states. This that the amplitude to be symmetric under interchange of particles or . Due to this symmetry we can determine two 1st level Feynman diagrams to describe this scattering.

The amplitudes of the individual Feynman diagrams add linearly to form the total amplitude

Using the Feynman rules, each vertex contribute a factor

and the propagator gives

where q is the momentum of the photon

and is the Mandelstam metric which allows the transformation from the contravariant to covariant form needed for tensor multiplication. Examining both Feynman diagrams seperately, we find for their individual amplitudes

Without loss of generality, we can extend this to the center of mass frame

Using the fact that