Configuration space for quantum gravity in a locally regularized path integral
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We discuss some aspects of the metric configuration space in quantum gravity in the background field formalism. We give a necessary and sufficient condition for the parametrization of Euclidean metric fluctuations such that (i) the signature of the metric is preserved in all configurations that enter the gravitational path integral, and (ii) the parametrization provides a bijective map between full Euclidean metrics and metric fluctuations about a fixed background. For the case of foliatable manifolds, we show how to parametrize fluctuations in order to preserve foliatability of all configurations. Moreover, we show explicitly that preserving the signature on the configuration space for the Lorentzian quantum gravitational path integral is most conveniently achieved by inequality constraints. We discuss the implementation of these inequality constraints in a nonperturbative renormalization group setup.
| Original language | English |
|---|---|
| Article number | 126002 |
| Journal | Physical Review D |
| Volume | 106 |
| Issue number | 12 |
| ISSN | 2470-0010 |
| DOIs | |
| Publication status | Published - 15 Dec 2022 |
Bibliographical note
Funding Information:
The authors thank Astrid Eichhorn for fruitful collaboration in earlier stages, and for many discussions during various phases of the project. The authors also thank Bianca Dittrich for constructive comments on the manuscript. During parts of this work, A. P. was supported by the Alexander von Humboldt Foundation, and M. S. was supported by a scholarship of the German Academic Scholarship Foundation as well as by the DFG under Grant No. EI/1037-1. The authors acknowledge support by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Colleges and Universities. M. S. gratefully acknowledges extended hospitality at Syracuse University, and at CP3-Origins at the University of Southern Denmark during various stages of this work.
Publisher Copyright:
© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
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