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A Primer of Group Theory for Loop Quantum Gravity and Spin-foams
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Calculations in Loop Quantum Gravity (LQG) and spin-foam theory rely heavily on the group theory of SU(2) and SL(2,C). Even though many monographs are devoted to this material, the various tools required (representation theory, harmonic analysis, recoupling theory, ...) are often scattered across different books, each with its own conventions and notations. This was the initial motivation for the present document, which serves three main purposes: a concise introduction for students to the essential mathematical tools of LQG, a convenient compendium of formulae for researchers, and a translation hub between the conventions of the main references. These notes are aimed both at physicists, who want their tools to be mathematically well-grounded, and at mathematicians, curious to see how some of their familiar abstract structures reveal the beauty of quantum gravity.
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Thermal $n$-Point Conformal Blocks in Four Dimensions from Oscillator Representations
New analytic formulas for four-dimensional thermal n-point conformal blocks are derived from oscillator representations, with a correct low-temperature limit to vacuum comb-channel blocks.
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