Show that the expansion (18.7) substituted into Eq. (18.1) gives a Lagrangian density for which there appear
Question:
Show that the expansion (18.7) substituted into Eq. (18.1) gives a Lagrangian density for which there appear to be five degrees of freedom: one from a massive scalar \(\eta\), one from a massive scalar \(\xi\), and three from a massive photon \(A_{\mu}\). Argue that this is unphysical because the original Lagrangian density had only four degrees of freedom. Show that the gauge transformation (18.8) eliminates the explicit \(\xi\) degree of freedom and that the resulting Lagrangian density is Eq. (18.9), with four degrees of freedom: one from a massive Higgs boson and three from a massive photon.
Data from Eq. 18.1
Data from Eq. 18.7
Data from Eq. 18.8
Data from Eq. 18.9
Step by Step Answer:
Symmetry Broken Symmetry And Topology In Modern Physics A First Course
ISBN: 9781316518618
1st Edition
Authors: Mike Guidry, Yang Sun