A. Zee, Quantum Field Theory in a Nutshell · Problem VIII.1.3

Field Theory Redux

Physics — QFT

Problem

Show that if

h_{\mu\nu}

does not satisfy the harmonic gauge, we can always make a gauge transformation with

\varepsilon_\nu

determined by

\partial^2\varepsilon_\nu = \partial_\mu h^\mu{}_\nu - \frac{1}{2}\partial_\nu h^\lambda{}_\lambda

so that it does. All of this should be conceptually familiar from your study of electromagnetism.