Loop Representations
arXiv:gr-qc/9312001 · doi:10.1007/3-540-58339-4_20
Abstract
The loop representation plays an important role in canonical quantum gravity because loop variables allow a natural treatment of the constraints. In these lectures we give an elementary introduction to (i) the relevant history of loops in knot theory and gauge theory, (ii) the loop representation of Maxwell theory, and (iii) the loop representation of canonical quantum gravity. (Based on lectures given at the 117. Heraeus Seminar, Bad Honnef, Sept. 1993)
38 pages, MPI-Ph/93-94
References in corpus (11)
- Weaving a classical geometry with quantum threads
- Representations of the holonomy algebras of gravity and non-Abelian gauge theories
- Jones Polynomials for Intersecting Knots as Physical States of Quantum Gravity
- How the Jones Polynomial Gives Rise to Physical States of Quantum General Relativity
- A Loop Representation for the Quantum Maxwell Field
- Unique determination of an inner product by adjointness relations in the algebra of quantum observables
- The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space
- Chen Integrals, Generalized Loops and Loop Calculus
- Loop Representations for 2+1 Gravity on a Torus
- The weaving of curved geometries
- Knot theory and quantum gravity in loop space: a primer