craigi said:
What are the best online introductory resources for Loop Quantum Gravity?
There was a thread about LQG introductory resources started about one year ago
https://www.physicsforums.com/showthread.php?t=676720
This came up in that thread. It is recent, has 85 pages and 20 figures, is online
http://arxiv.org/abs/1402.3586
Sundance Bilson-Thompson, Deepak Vaid
School of Chemistry and Physics, University of Adelaide, Adelaide SA, Australia
Department of Physics, National Institute of Technology Karnataka (NITK), Surathkal, Karnataka, India
Abstract: We present a pedagogical introduction to the notions underlying the connec- tion formulation of General Relativity - Loop Quantum Gravity (LQG) - with an emphasis on the physical aspects of the framework. We begin by reviewing General Relativity and Quantum Field Theory, to emphasise the similarities between them which establish a foun- dation upon which to build a theory of quantum gravity. We then explain, in a concise and clear manner, the steps leading from the Einstein-Hilbert action for gravity to the construction of the quantum states of geometry, known as
spin-networks, which provide the basis for the kinematical Hilbert space of quantum general relativity. Along the way we introduce the various associated concepts of
tetrads, spin-connection and holonomies which are a pre-requisite for understanding the LQG formalism. Having provided a minimal introduction to the LQG framework, we discuss its applications to the problems of black hole entropy and of quantum cosmology. A list of the most common criticisms of LQG is presented, which are then tackled one by one in order to convince the reader of the physical viability of the theory.
An extensive set of appendices provide accessible introductions to several key notions such as the
Peter-Weyl theorem, duality of differential forms and Regge calculus, among others. The presentation is aimed at graduate students and researchers who have some familiarity with the tools of quantum mechanics and field theory and/or General Relativity, but are intimidated by the seeming technical prowess required to browse through the existing LQG literature. Our hope is to make the formalism appear a little less bewildering to the un-initiated and to help lower the barrier for entry into the field.
sundance.bilson-thompson@adelaide.edu.au
deepak@nitk.edu.in
There are other introductory resources. I can't list them, but you could try this one and see if it is right for you. If not, say how this one does not fit your needs and ask again. We can try to suggest something else that is closer to what you want. So maybe by successive approximation we will get a good fit