Quantum Electrodynamics

Abstract

Link to: physicspages home page. To leave a comment or report an error, please use the auxiliary blog. Post date: 17 Nov 2018. References: Amitabha Lahiri & P. B. Pal, A First Book of Quantum Field Theory, Second Edition (Alpha Science International, 2004) Chapter 9, Exercise 9.8. We’ve seen that in quantum electrodynamics, no first-order scattering processes are possible, since we cannot conserve 4-momentum in such processes. However, in the case where a fermion (such as an electron) is scattered by a heavy nucleus, or by some static external electric field, we can get an approximation for the scattering amplitude by neglecting the momentum transferred from the scattered particle to the nucleus. In other words, we assume that the nucleus remains at rest (in the lab frame) throughout the scattering process. This is done by splitting the electric vector potential into two parts: one part Aeμ represents the external field (with the subscript e standing for ’external’) and the other part Aμ being the usual vector potential with which we have dealt in earlier posts. This means we can write the interaction term in the Lagrangian as