Higher-order curvature operators like R□R add new poles and shift existing ones in the graviton propagator, with a method to correctly derive the Einstein frame action illustrated for f(R) gravity.
Living with Ghosts
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
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, $\phi$ and $\Box \phi $ 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 $\phi$ and $\phi_{,\tau}$. To calculate probabilities for observations, one has to trace out over $\phi_{,\tau}$ 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 theory, as the coefficient of the fourth order term in the action tends to zero. Hence unitarity is restored at the low energies that now occur in the universe.
representative citing papers
Weyl geometry is equivalent to Riemannian geometry of a non-local dressed metric g*_{\mu\nu} via Wilson lines, with the quadratic and WDBI actions taking the same form in the symmetric phase.
citing papers explorer
-
Weyl conformal geometry vs Riemannian geometry of Weyl gauge invariant dressed metric
Weyl geometry is equivalent to Riemannian geometry of a non-local dressed metric g*_{\mu\nu} via Wilson lines, with the quadratic and WDBI actions taking the same form in the symmetric phase.
- The fall and the rise of Weyl gauge theory