On the structure of the space of generalized connections

Abstract

We give a modern account of the construction and structure of the space of generalized connections, an extension of the space of connections that plays a central role in loop quantum gravity.

30 pages, added references, minor changes. To appear in International Journal of Geometric Methods in Modern Physics

References in corpus (7)

• Background Independent Quantum Gravity: A Status Report
• Lectures on Loop Quantum Gravity
• The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
• How far are we from the quantum theory of gravity?
• Separable Hilbert space in Loop Quantum Gravity
• Diffeomorphism covariant representations of the holonomy-flux star-algebra
• On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories

Cited by in corpus (13)

• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• Non-commutative flux representation for loop quantum gravity
• The Quantum Configuration Space of Loop Quantum Cosmology
• Loop Quantum Geometry: A primer
• The Koslowski-Sahlmann representation: Quantum Configuration Space
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• On the space of generalized fluxes for loop quantum gravity
• Functorial Aspects of the Space of Generalized Connections
• A quantum kinematics for asymptotically flat spacetimes
• Local Properties of Measures in Quantum Field Theory and Cosmology
• AQV II. A new formulation of the Weyl C*-algebra
• Groups of generalized flux transformations in the space of generalized connections
• Denseness of Ashtekar-Lewandowski states and a generalized cut-off in loop quantum gravity