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Don’t throw the baby out with the bath water

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Abstract

I stress the importance of retaining a healthy classical limit while we search for an ultraviolet completion to quantum gravity. A key problem with negative-norm quantizations of higher-derivative Lagrangians is that their classical limits do not correspond to real-valued metrics evolving in a real-valued spacetime. I also demonstrate that no completion based on the flat spacetime background S-matrix can suffice by providing an explicit example of a theory with unit S-matrix which still shows interesting changes in single-particle kinematics and in the evolution of its background. I discuss the implications of these considerations for the program of Asymptotic Safety. Finally, I urge that some attention be given to the possibility that quantum general relativity might make sense if only we could go beyond conventional perturbation theory.

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Data Availability Statement

No data are associated in the manuscript.

Notes

  1. The normalization factor is,

    $$\begin{aligned} N = \sqrt{\frac{m}{\pi \hbar }} \Bigl [ \sqrt{g} (1 \!-\! 2\sqrt{g})\Bigr ]^{\frac{1}{4}} \;. \nonumber \end{aligned}$$

  2. I thank Arkady Tseytlin for this observation.

  3. Note that this immediately explains the mass (36).

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Acknowledgements

I am grateful for civil discussion and correspondence on this subject with J. F. Donoghue, B. Holdom and P. D. Mannheim. This work was supported by NSF grant PHY-2207514 and by the Institute for Fundamental Theory at the University of Florida.

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    R. P. Woodard

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Dedicated to the memory of Stanley Deser: teacher, mentor, friend.

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Woodard, R.P. Don’t throw the baby out with the bath water. Eur. Phys. J. Plus 138, 1067 (2023). https://doi.org/10.1140/epjp/s13360-023-04709-4

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