Ward identities in a general axial gauge. II. Quantum gravity

Abstract

We have calculated the pole part of the one-loop graviton self-energy in the noncovariant axial gauge ${n}_{\ensuremath{\mu}}{\ensuremath{\varphi}}_{\ensuremath{\mu}\ensuremath{\nu}}=0$, ${n}^{2}\ensuremath{\ne}0$, where ${\ensuremath{\varphi}}_{\ensuremath{\mu}\ensuremath{\nu}}$ is the physical gravition field and ${n}_{\ensuremath{\mu}}$ is an arbitrary but constant vector. It is shown that the self-energy is, unexpectedly, both nontransverse and ${n}_{\ensuremath{\mu}}$ dependent, even though it satisfies the correct gravitational Ward identity. This Ward identity is found to contain a term corresponding to a "pincer" Feynman diagram which is directly responsible for the nontransversality of the graviton self-energy. Ghost particles do not contribute to the graviton amplitude. All aixal-gauge integrals are consistently evaluated in the context of dimensional regularization and by applying the principal-value prescription.