Unitary Quadratic Quantum Gravity in 4D

Abstract

In quadratic gravity, with a positive Weyl squared coefficient, the extra spin-2 sector is shown to correspond to a dual inverted harmonic oscillator, instead of a ghost. Using the Wightman spectrum condition, we prove that the associated K\"{a}ll\'{e}n--Lehmann spectral density vanishes, reflecting the absence of a normalizable ground state and the spacelike nature of the propagator pole. This uniquely fixes the propagator to a principal value form as a theorem, not a prescription. The optical theorem is satisfied, the dual IHO spin-2 is not an asymptotic state, and gives only virtual contributions at all loop orders. As a result, unitarity is preserved consistently with renormalizability.