Quadratic gravity in 4D preserves unitarity because the extra spin-2 sector is a dual inverted harmonic oscillator with vanishing spectral density, yielding a principal-value propagator that satisfies the optical theorem with only virtual contributions.
Writingk µ =aP µ +k µ ⊥ withP·k ⊥ = 0givesa= 1/2, then k2 ⊥ =µ 2 2 − P 2 4 .(21) The branch point (pinch atkµ ⊥ = 0) is at P 2 ∗ = 4µ2 2 >0(which is spacelike)
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Unitary Quadratic Quantum Gravity in 4D
Quadratic gravity in 4D preserves unitarity because the extra spin-2 sector is a dual inverted harmonic oscillator with vanishing spectral density, yielding a principal-value propagator that satisfies the optical theorem with only virtual contributions.