Covariant singularities in quantum field theory and quantum gravity
Abstract
It is rather wellknown 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 illdefined 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 pathintegral measure is regular in any fourdimensional theory of gravity without matter or in any theory in which gravity is either absent or treated semiclassically. 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 modelindependent classification of functional singularities using homotopy groups and we discuss examples of theories with and without such singularities.
 Publication:

Nuclear Physics B
 Pub Date:
 October 2021
 DOI:
 10.1016/j.nuclphysb.2021.115496
 arXiv:
 arXiv:2102.10688
 Bibcode:
 2021NuPhB.97115496C
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 Accepted for publication in Nucl. Phys. B