Covariant singularities in quantum field theory and quantum gravity

Roberto Casadio (Dipartimento di Fisica e Astronomia, Università di Bologna, Bologna, Italy; I.N.F.N., Sezione di Bologna, Bologna, Italy) ; Alexander Kamenshchik (Dipartimento di Fisica e Astronomia, Università di Bologna, Bologna, Italy; I.N.F.N., Sezione di Bologna, Bologna, Italy; L.D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences, Moscow, Russia) ; Iberê Kuntz (Dipartimento di Fisica e Astronomia, Università di Bologna, Bologna, Italy; I.N.F.N., Sezione di Bologna, Bologna, Italy)

It is rather well-known that spacetime singularities are not covariant under field redefinitions. A manifestly covariant approach to singularities in classical gravity was proposed in [1]. In this paper, we start to extend this analysis to the quantum realm. We identify two types of covariant singularities in field space corresponding to geodesic incompleteness and ill-defined path integrals (hereby dubbed functional singularities). We argue that the former might not be harmful after all, whilst the latter makes all observables undefined. We show that the path-integral measure is regular in any four-dimensional theory of gravity without matter or in any theory in which gravity is either absent or treated semi-classically. This might suggest the absence of functional singularities in these cases, however it can only be confirmed with a thorough analysis, case by case, of the path integral. We provide a topological and model-independent classification of functional singularities using homotopy groups and we discuss examples of theories with and without such singularities.

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      "value": "It is rather well-known that spacetime singularities are not covariant under field redefinitions. A manifestly covariant approach to singularities in classical gravity was proposed in [1]. In this paper, we start to extend this analysis to the quantum realm. We identify two types of covariant singularities in field space corresponding to geodesic incompleteness and ill-defined path integrals (hereby dubbed functional singularities). We argue that the former might not be harmful after all, whilst the latter makes all observables undefined. We show that the path-integral measure is regular in any four-dimensional theory of gravity without matter or in any theory in which gravity is either absent or treated semi-classically. This might suggest the absence of functional singularities in these cases, however it can only be confirmed with a thorough analysis, case by case, of the path integral. We provide a topological and model-independent classification of functional singularities using homotopy groups and we discuss examples of theories with and without such singularities."
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Published on:
29 September 2021
Publisher:
Elsevier
Published in:
Nuclear Physics B , Volume 971 C (2021)

Article ID: 115496
DOI:
https://doi.org/10.1016/j.nuclphysb.2021.115496
Copyrights:
The Authors
Licence:
CC-BY-3.0

Fulltext files: