Loops, Knots, Gauge Theories and Quantum Gravity
Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. This text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. The book begins with a detailed review...
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A self-contained introduction to applications of loop representations and knot theory in quantum gravity.
ForewordPreface1Holonomies and the group of loops12Loop coordinates and the extended group of loops293The loop representation524Maxwell theory885Yang-Mills theories1136Lattice techniques1317Quantum gravity1618The loop representation of quantum gravity1889Loop representation: further developments20910Knot theory and physical states of quantum gravity23811The extended loop representation of quantum gravity27512Conclusions, present status and outlook302References309Index319
