It is rather well-known that spacetime singularities are not covariant under field redefinitions. A mani- festly 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 singu- larities). 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 sug- gest 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.

Casadio, R., Kamenshchik, A., Kuntz, I. (2021). Covariant singularities in quantum field theory and quantum gravity. NUCLEAR PHYSICS. B, 971, 1-30 [10.1016/j.nuclphysb.2021.115496].

Covariant singularities in quantum field theory and quantum gravity

Casadio, Roberto;Kamenshchik, Alexander;Kuntz, Iberê
2021

Abstract

It is rather well-known that spacetime singularities are not covariant under field redefinitions. A mani- festly 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 singu- larities). 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 sug- gest 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.
2021
Casadio, R., Kamenshchik, A., Kuntz, I. (2021). Covariant singularities in quantum field theory and quantum gravity. NUCLEAR PHYSICS. B, 971, 1-30 [10.1016/j.nuclphysb.2021.115496].
Casadio, Roberto; Kamenshchik, Alexander; Kuntz, Iberê
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/828944
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