Unitary Quadratic Quantum Gravity in 4D

• URL: http://arxiv.org/abs/2604.19707v2
• Date: Thu, 23 Apr 2026 14:53:13 GMT
• Title: Unitary Quadratic Quantum Gravity in 4D
• Abstract summary: We prove that the associated Kllén--Lehmann spectral density vanishes, reflecting the absence of a normalizable ground state.<n>This uniquely fixes the propagator to a principal value form as a theorem, not a prescription.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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