Gambini R., Pullin J. A First Course in Loop Quantum Gravity

Oxford University Press, Inc., New York, 2011. — 192 p. — ISBN: 9780199590759.Loop quantum gravity has emerged as a possible avenue towards the quantization of general relativity. Looking at the top 50 cited papers of all time of the arXiv.org:gr-qc preprint repository (which includes papers on gravity as a whole, not only quantum gravity); according to the SPIRES
database in SLAC in its latest edition (2006) one finds that 13 papers are on loop quantum gravity. Although a smaller field than string theory, the other main approach to quantum gravity pursued today, the number of researchers working in loop quantum gravity is significant. At the moment both string theory and loop quantum gravity remain incomplete paradigms and as a consequence controversies about which is a more promising approach naturally arise. We will address some of these in this book.Why quantize gravity?
Special relativity and electromagnetism
Some elements of general relativity
Hamiltonian mechanics including constraints and fields
Yang-Mills theories
Quantum mechanics and elements of quantum field theory
General relativity in terms of Ashtekar's new variables
Loop representation for general relativity
An application: loop quantum cosmology
Further developments
Open issues and controversies