Groups of generalized flux transformations in the space of generalized connections

TL;DR

This paper introduces a new group of transformations in the space of generalized connections, extending flux transformations in loop quantum gravity by incorporating functions on directions and germs of curves.

Contribution

It defines a novel group of flux-related transformations in generalized connections, broadening the scope of symmetries in loop quantum gravity.

Findings

The group includes transformations generated by flux variables.

It is labeled by SU(2)-valued functions on directions.

Further generalization involves functions depending on germs of curves.

Abstract

We present a group of transformations in the space of generalized connections that contains the set of transformations generated by the flux variables of loop quantum gravity. This group is labelled by certain SU(2)-valued functions on the bundle of directions in the spatial manifold. A further generalization is obtained by considering functions that depend on germs of analytic curves, rather than just on directions.