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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We construct the smeared diffeomorphism constraint operator at finitetriangulation from the basic holonomy- flux operators of Loop Quantum Gravity,evaluate its continuum limit on the Lewandowski- Marolf habitat and show thatthe action of the continuum operator provides an anomaly free representation ofthe Lie algebra of diffeomorphisms of the 3- manifold. Key features of ouranalysis include: (i) finite triangulation approximants to the curvature,$F_{ab}^i$ of the Ashtekar- Barbero connection which involve not only smallloop holonomies but also small surface fluxes as well as an explicit dependenceon the edge labels of the spin network being acted on (ii) the dependence ofthe small loop underlying the holonomy on both the direction and magnitude ofthe shift vector field (iii) continuum constraint operators which do {\em not}have finite action on the kinematic Hilbert space, thus implementing a keylesson from recent studies of parameterised field theory by the authors.  Features (i) and (ii) provide the first hints in LQG of a conceptualsimilarity with the so called "mu- bar" scheme of Loop Quantum Cosmology. Weexpect our work to be of use in the construction of an anomaly free quantumdynamics for LQG.

The Diffeomorphism Constraint Operator in Loop Quantum Gravity