# Friday 18 June 2021

14h00 – 15h00,

### Solution to the ghost problem in higher derivative gravity

#### Philip D. Mannheim (University of Connecticut)

While one can construct c-number propagators as matrix elements of q-number operators between quantum states in a quantum Hilbert space, one cannot go the other way round and construct the Hilbert space starting from the c-number propagator. Starting from the quantum Hilbert space of fourth-order derivative theories Bender and Mannheim [PRL 100, 110402 (2008), PRD 78, 025022 (2008)]) constructed the c-number propagator and found that it was not given by the matrix element between the vacuum and its Hermitian conjugate (as had previously been presupposed) but by the matrix element between the vacuum and its CPT conjugate, with there then being no ghosts states of negative norm. While the overlap of a state with its Hermitian conjugate might be negative the correct inner product is the overlap of a state with its CPT conjugate, and none of these overlaps are negative. Thus rather than get rid of the ghost states Bender and Mannheim showed that they actually were never there in the first place. Consequently, the fourth-order derivative conformal gravity theory is unitary. And since it is also renormalizable it provides a consistent quantum gravity theory in four spacetime dimensions.

https://univ-amu-fr.zoom.us/j/91448970216?pwd=SzhmcmRmVmpIY2l0a0JRSUpNdyszdz09

June 2021 :