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 describe a method of construction of gauge-invariant operators (Diracobservables or ``evolving constants of motion'') from the knowledge of theeigenstates of the gauge generator in time-reparametrization invariantmechanical systems. These invariant operators evolve unitarily with respect toan arbitrarily chosen time variable. We emphasize that the dynamics isrelational, both in the classical and quantum theories. In this framework, weshow how the ``emergent Wentzel-Kramers-Brillouin time'' often employed inquantum cosmology arises from a weak-coupling expansion of invariant transitionamplitudes, and we illustrate an example of singularity avoidance in a vacuumBianchi I (Kasner) model.

Construction of quantum Dirac observables and the emergence of WKB time