
TL;DR
This paper investigates higher derivative gravity theories, demonstrating that a path integral approach avoids ghost states and restores unitarity at low energies, contrasting with canonical methods.
Contribution
It introduces a path integral formulation for higher derivative scalar theories that prevents ghost states and restores unitarity at low energies.
Findings
Path integral approach avoids negative norm states.
Unitarity is restored as higher derivative terms diminish.
Transition probabilities match second order theory at low energies.
Abstract
Perturbation theory for gravity in dimensions greater than two requires higher derivatives in the free action. Higher derivatives seem to lead to ghosts, states with negative norm. We consider a fourth order scalar field theory and show that the problem with ghosts arises because in the canonical treatment, and are regarded as two independent variables. Instead, we base quantum theory on a path integral, evaluated in Euclidean space and then Wick rotated to Lorentzian space. The path integral requires that quantum states be specified by the values of and . To calculate probabilities for observations, one has to trace out over on the final surface. Hence one loses unitarity, but one can never produce a negative norm state or get a negative probability. It is shown that transition probabilities tend toward those of the second order…
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