By Rodolfo Gambini
This article offers a self-contained advent to functions of loop representations and knot conception in particle physics and quantum gravity. Loop representations (and the comparable subject of knot idea) are of substantial present curiosity simply because they supply a unified area for the examine of the gauge invariant quantization of Yang-Mills theories and gravity, and recommend a promising method of the eventual unification of the 4 basic forces. this article starts with a evaluate of calculus in loop house and the basics of loop representations. It then is going directly to describe loop representations in Maxwell concept, Yang-Mills theories in addition to lattice recommendations. purposes in quantum gravity are then mentioned intimately. Following chapters flow directly to think of knot concept, the braid algebra and prolonged loop representations in quantum gravity. a last bankruptcy assesses the present prestige of the idea and issues out attainable instructions for destiny examine. This self-contained advent could be of curiosity to graduate scholars and researchers in theoretical physics and utilized arithmetic.