A Primer of Group Theory for Loop Quantum Gravity and Spin-foams

Pierre Martin-Dussaud

Published 2019-02-22Version 1

Calculations in Loop Quantum Gravity (LQG) and spin-foams theory rely heavily on group theory of SU(2) and SL2(C). Even though many monographs exist devoted to this theory, the different tools needed (e.g. representation theory, harmonic analysis, recoupling theory...) are often dispersed in different books and with different conventions and notations. This has initially motivated the compilation of the present document. Nowadays, these notes can serve three main purposes: a concise introduction for students to the essential mathematical tools of LQG, a convenient compendium for researchers, a translational hub between the conventions of the main references. These notes are aimed both at physicists, caring about their tools to be mathematically well grounded, and at mathematicians, curious about how some of their familiar abstract structures can reveal the beauty of quantum gravity.