Loop Representations

TL;DR

This paper provides an introductory overview of loop representations in quantum gravity, covering their historical development, application to Maxwell theory, and role in canonical quantum gravity, emphasizing their importance in constraint management.

Contribution

It offers an accessible introduction to loop representations, connecting knot theory, gauge theory, and quantum gravity, highlighting their conceptual and practical significance.

Findings

Loop variables facilitate natural constraint handling in quantum gravity

Loop representation connects knot theory with gauge and gravity theories

Educational overview based on lectures from 1993

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)