English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The quantization of Lorentzian or Euclidean 2+1 gravity by canonical methodsis a well-studied problem. However, the constraints of 2+1 gravity are those ofa topological field theory and therefore resemble very little those of thecorresponding Lorentzian 3+1 constraints. In this paper we canonically quantizeEuclidean 2+1 gravity for arbitrary genus of the spacelike hypersurface withnew, classically equivalent constraints that maximally probe the Lorentzian 3+1situation. We choose the signature to be Euclidean because this implies thatthe gauge group is, as in the 3+1 case, SU(2) rather than SU(1,1). We employ,and carry out to full completion, the new quantization method introduced inpreceding papers of this series which resulted in a finite 3+1 Lorentzianquantum field theory for gravity. The space of solutions to all constraintsturns out to be much larger than the one as obtained by traditional approaches,however, it is fully included. Thus, by suitable restriction of the solutionspace, we can recover all former results which gives confidence in the newquantization methods. The meaning of the remaining "spurious solutions" isdiscussed.Comment: 35p, LATE

Quantum spin dynamics (QSD): IV. Euclidean quantum gravity as a model to test Lorentzian quantum gravity