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

Transcribed Image Text:

L = (D) (D) * A(*)F 4