A. Zee, Quantum Field Theory in a Nutshell · Problem IV.6.6

Field Theory Redux

Physics — QFT

Problem

Derive (14). [Hint: The procedure is exactly the same as that used to obtain (III.4.9).] Write

L = \frac{1}{2}A_\mu Q^{\mu\nu}A_\nu + \ldots

with

Q_{\mu\nu} = (\partial^2 + M^2)g_{\mu\nu} - [1 - (1/\xi)]\partial_\mu\partial_\nu

or in momentum space

Q_{\mu\nu} = -(k^2 - M^2)g_{\mu\nu} + [1 - (1/\xi)]k_\mu k_\nu

. The propagator is the inverse of

Q_{\mu\nu}