Gauge invariance and unitarity in higher-derivative quantum gravity

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Abstract
The question of unitarity is examined in the renormalizable, ‘‘higher-derivative’’ theory of quantum gravity. It is pointed out that the presence of a massive spin-2 ghost in the bare propagator is inconclusive, since this excitation is unstable. In the presence of unstable particles, expansions using bare propagators are impossible—modified expansions with dressed propagators that exhibit the complex nature of the unstable pole must be employed. It is found, however, that the position of the complex poles in the dressed propagator is explicitly gauge dependent. It turns out that this is a specifically gravitational effect; it does not occur in gauge theories with an internal-symmetry gauge group. On the other hand, a physical S matrix between in and out states containing only transverse, massless gravitons and physical massless matter fields is shown to be gauge independent. It then follows by a standard, albeit formal, argument that the contribution of all gauge-variant poles to its intermediate states must cancel. The physical S matrix should therefore, be unitary. In this development, the standard rules of quantum field theory are followed throughout; no ad hoc modifications, such as the Lee-Wick prescription, are ever invoked.

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