- #1

boltzman1969

- 7

- 1

I am self-teaching Quantum Elctrodynamics, and have come across something which I do not understand. I would appreciate feedback from anyone on this specific issue from Atchison & Hey, "Guage Theories in Particle Physics" pg 238-239:

In calculating the u-channel electron-muon scattering amplitude at the one-photon exchange, one can simplify the calculation by introducing the electron and muon tensors:

L

^{μγ}M

_{μγ}, where

L

^{μγ}= 2[k'

_{μ}k

_{γ}+k'

_{γ}k

_{μ}+(q

^{2}/2)g

^{μγ}] (electron tensor) and

M

^{μγ}= 2[p'

_{μ}p

_{γ}+p'

_{γ}p

_{μ}+(q

^{2}/2)g

^{μγ}] (muon tensor)

Now q

^{μ}= (k-k')

^{μ}= (p-p')

^{μ}is the 4-momentum of the exchanged photon; p, p' are the intial and final momenta of the muon; k, k' the initial and final 4-momenta of the electron.

It is claimed that q

^{μ}L

_{μγ}= q

^{γ}L

_{μγ}= 0, which is fine because L is the product of 2 4-currents and q

^{μ}j

_{μ}

^{e-}= 0. However, according to the text that I am reading, the q

^{μ}L

_{μγ}= q

^{γ}L

_{μγ}condition implies that we can replace p' in the muon tensor with (p+q); ie, M

_{effective}= 2[2p

_{μ}p

_{γ}+ (q

^{2}/2)g

^{μγ}.

Does anyone know how to go from the condition q

^{μ}L

_{μγ}= 0 to the constraint condition p' = (p+q)?

Thank you in advance for your assistance.