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.
Covariant singularities in quantum field theory and quantum gravity / Casadio, Roberto; Kamenshchik, Alexander; Kuntz, Iberê. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - ELETTRONICO. - 971:(2021), pp. 115496.1-115496.30. [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.File | Dimensione | Formato | |
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