Unfolding the singularities in superspace
type: Item
instance of: scholarly article
title: Unfolding the singularities in superspace
zbMATH Open document ID: 0541.58012
DOI: 10.1007/BF00761583
author: Arthur E. Fischer
published in: General Relativity and Gravitation
publication date: 1983-01-01T00:00:00Z
review text: The superspace of a three dimensional compact connected Riemannian manifold M is the space of all Riemannian geometries of M modulo the group of diffeomorphisms of M. The superspace is the configuration space for the dynamical formulation of classical general relativity and the domain space for the quantum mechanical state functional in quantum gravity. The superspace is not a manifold, having singularities arising from the varying dimensions of the isometry groups of the different metrics. Here a construction is described for unfolding the singularities of superspace. The resulting (unfolded) space is a singularity free infinite dimensional manifold and the construction is natural, covariant with respect to all coordinate transformations, and it does not exclude any particular highly symmetrical solution from superspace. The relationship between the proposed unfolding construction and a previous one based on the choice of a particular point is also discussed.
Mathematics Subject Classification ID: 58K35
Mathematics Subject Classification ID: 58D17
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83E05
zbMATH DE Number: 3860022
zbMATH Keywords: superspace
zbMATH Keywords: singularities
zbMATH Keywords: unfolding construction
MaRDI profile type: Publication
cites work: Q5527782
cites work: Quantum Theory of Gravity. I. The Canonical Theory
cites work: Groups of diffeomorphisms and the motion of an incompressible fluid
cites work: The primary decomposition theory for modules
cites work: Q5617487
cites work: Q3846750
cites work: Q5731354
cites work: The classification of 𝐺-spaces
cites work: A new definition of singular points in general relativity
description: scientific article; zbMATH DE number 3860022