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

A notion of effective gauge fields which does not involve a background metricis introduced. The role of scale is played by cellular decompositions of thebase manifold. Once a cellular decomposition is chosen, the corresponding spaceof effective gauge fields is the space of flat connections with singularitieson its codimension two skeleton, ${\cal A}_{C-flat} \subset \bar{\cal A}_M$. Ifcellular decomposition $C_2$ is finer than cellular decomposition $C_1$, thereis a coarse graining map $\pi_{C_2 \to C_1}: {\cal A}_{C_2-flat} \to {\calA}_{C_1-flat}$. We prove that the triple $({\cal A}_{C_2-flat}, \pi_{C_2 \toC_1}, {\cal A}_{C_1-flat})$ is a principal fiber bundle with a preferred globalsection given by the natural inclusion map $i_{C_1 \to C_2}: {\calA}_{C_1-flat} \to {\cal A}_{C_2-flat}$.  Since the spaces ${\cal A}_{C-flat}$ are partially ordered (by inclusion) andthis order is directed in the direction of refinement, we can define acontinuum limit, $C \to M$. We prove that, in an appropriate sense, $\lim_{C\to M} {\cal A}_{C-flat} = \bar{\cal A}_M$. We also define a construction ofmeasures in $\bar{\cal A}_M$ as the continuum limit (not a projective limit) ofeffective measures.Comment: 29 pages, 2 figure

Geometry of C-flat connections, coarse graining and the continuum limit