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Jonathan Oppenheim @postquantum.bsky.social · 17/09/2024

The PQCG action has higher derivative terms (hence it is renormalisable) but because it is computing a probability and not an amplitude, it doesn't suffer from negative norm ghosts or tachyons (which is what plagues higher derivative theories of quantum gravity). 3/

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Jonathan Oppenheim @postquantum.bsky.social · 17/09/2024

Here is the path integral for Brownian motion straight out of Feynman and Hibbs. It has higher derivatives, but just describes a free particle being hit by random forces. On average the acceleration (q double dot) is zero, but there are contributions away from this. 4/

$The path integral for Brownian motion (action \ddot{q]), vs the quantum path integral. The Brownian motion path integral doesn't have ghosts!$

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Jonathan Oppenheim @postquantum.bsky.social · 17/09/2024

So classically, higher derivative actions are fine, but in quantum theory, higher derivatives in the action spell trouble (Ostragradsky's instability which implies negative norm "ghosts"). The preprint is available at arxiv.org/abs/2402.17844. 5/5

arxiv.org

Renormalisation of postquantum-classical gravity

One of the obstacles to reconciling quantum theory with general relativity, is constructing a theory which is both consistent with observation, and and gives finite answers at high energy, so that...

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