Unitary Quadratic Quantum Gravity in 4D

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 Källén--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.