Bodendorfer Norbert. An Elementary Introduction to Loop Quantum Gravity

Faculty of Physics, University of Warsaw, arXiv, 2016. — 62 p.An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in five lectures, including exercises, and requires only little prior knowledge of quantum mechanics, gauge theory, and general relativity.
From the contents:
Why (loop) quantum gravity
Motivations for studying quantum gravity,
Possible scenarios for observations,
Approaches to quantum gravity,
General comments on the canonical quantisation programme,
Arguments for canonical loop quantum gravity,
Criticism of canonical loop quantum gravity,
Exercises.
Elements of loop quantum gravity through cosmology
Preliminaries,
Classical dynamics,
Wheeler-de Witt quantization,
Loop quantum cosmology,
Kinematical scalar products and ordering,
Superselection and superpositions,
Outlook on full theory,
Exercises.
General relativity in the connection formulation and quantum kinematics
Canonical general relativity,
Connection variables,
Holonomies and fluxes,
Quantisation,
Outlook,
Exercises.
Geometric operators, matter, and quantum geometry
Area operator,
Volume operator,
Quantum geometry,
Matter,
Exercises.
Quantum dynamics and outlook
Dynamics,
Open questions and future directions,
Exercises.