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 of loop representation theory. It then goes on to describe loop representations in Maxwell theory, Yang-Mills theories, as well as lattice techniques. The authors then discuss applications in quantum gravity in detail. Following chapters consider knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research.
Author(s): Rodolfo Gambini, Jorge Pullin
Series: Cambridge Monographs on Mathematical Physics
Publisher: Cambridge University Press
Year: 2009
Language: English
Pages: 340
City: Cambridge
frontmatter
dedication
/core/services/aop-cambridge-core/content/view/5A3B889165D3044C694AC742DCAC5192/9781009290197toc_ix-xii.pdf/contents.pdf
cambridge.org
Loops, Knots, Gauge Theories and Quantum Gravity
foreword
preface
holonomies_and_the_group_of_loops
loop_coordinates_and_the_extended_group_of_loops
loop_representation
maxwell_theory
yangmills_theories
lattice_techniques
quantum_gravity
loop_representation_of_quantum_gravity
loop_representation_further_developments
knot_theory_and_physical_states_of_quantum_gravity
extended_loop_representation_of_quantum_gravity
conclusions_present_status_and_outlook
references
index
